[EDIT: Formatted and updated slightly here: https://docs.google.com/document/d/1d4csDu-Wro1P4G67ogLpDWFdnIZjaLtRQNrjxDBp3eQ/edit#heading=h.u0ovlynh7nmc]

GENERAL NOTES

1. Make sure you beat the game at least once normally before attempting a run, including unlocking all levels and getting all optional upgrades. This category goes through all of the content of the game on a preexisting file that has everything unlocked. It is not necessary to 100% the game (all badges and collectables), just to have all levels and upgrades unlocked. This guide assumes you have played through the game casually.
2. It is easier for most players to select the option that puts the number of unused platforms over your head (which is not on by default). Also make sure to select the option to make the speedrunning timers visible.
3. Pay attention to the number of hearts you have left when reaching a checkpoint or an easily accessible heart bulb. If you are on your last heart, it is almost always faster to just die immediately after reaching a checkpoint to reset yourself to 4 hearts than it would be to die later in the level. On a similar note, it is frequently worth it to get extra heart bulbs if you took damage earlier in the level.
4. If you need to change the controls from the default controls in the game for any reason, or have a controller whose default controls are like this, make sure that any button used to place a platform can only be hard pressed and not partially pressed. Boost jumping and most other tricks in the game require a full press of the platform button, and not a partial press.
5. Unless you don't value your sanity, play on normal difficulty. It is faster anyway because of gaining access to hearts to be able to do damage boosts, laser warps, and to make mistakes.

GENERAL TRICKS

These tricks are relevant to several levels. Note that new strategies are frequently discovered, so this is not a comprehensive list. Strats that are only relevant to one stage are mentioned later. Many strats are simply too difficult for the amount of time they save to be worth learning until you have the easier strats mastered.

1. Damage boost - There are a few moments of invincibility after you take damage. You can use the invincibility frames to move through enemies that would otherwise be blocking your path.
2. Laser warp - If you take damage from a laser and are in the air (not on your own platform), the game will place you on the last ground you touched that was considered "safe." There are a few levels that take advantage of this to save the amount of time it would normally take to backtrack segments of a level.
3. Boost jumping - This takes a decent amount of practice to master, but is worth it. It is performed by jumping in the few frames after placing a platform and before the platform appears to be there. Several of them can be chained together to climb large distances in levels where a lot of platforms are given to you. Boost jumping for smaller distances is helpful to save frames here and there, and is also necessary for some tricks specific to some levels.
4. Peak jumps - There are a few platforms that aren't intended to be reached normally, but can be reached with a precise placement of one or more platforms at the very peak of where they could be placed. Some of these seem to be animation dependent, so require multiple tries once at the last platform.
5. Pixel jumps - There are a few levels that have a platform under a laser, where the platform is just a couple pixels longer than the laser. This trick is very precise, but it is possible to land on these pixels to regain your platforms. In a couple of levels, you can do a minor skip with a pixel jump.
6. Platform cancelling - If a platform is placed at a time when you only have downward momentum (no upward momentum), you can cancel it quickly by tapping the platform button. This can be used to save tiny bits of time here and there, but also could be used for some other tricks such as landing quickly before being shot upwards with a slingshot to get your platforms back.
7. Slingshot boost - Timing a jump when the shot of the slingshot hits you back will cause the game to add both momentums together and you will gain a lot more height than the intended strategy of standing still on your platform. There are several places where you can skip portions of levels this way. A few slingshot skips are finicky in the sense of requiring precise maneuvering on the ascent, such as those in 2-8. In stages where you have multiple platforms, you can also place 2 shots one after the other and let both of them hit you on the way up.
8. Platform hoarding - In levels where enemies exist that give you platforms for killing them, it is possible in many places to hoard additional platforms. These levels have a convenient place where either there are more than one platform granting enemy nearby, or where you can hold the platform to kill the enemy as it respawns and be touching solid ground at the same time.
9. Bubble mechanics - In 5-2 and 5-4, the bubbles will give you a platform back (up to the max for the level) if you hit them from any angle. Which means you can gain platforms from jumping and hitting them from underneath or the sides. When above them, if you hit jump at the right moment upon landing on them (pretty sure this is frame perfect), you will get extra height with your jump.
10. Loading platform manipulation - In many levels, it is possible with precise movement to not deactivate one of these platforms where the developer intended for you to do so. This allows for minor skips in levels where this is relevant.
11. Laser jumps - Some lasers in the game look like a solid bar with a moving wire spiraled around them. On these lasers, it is possible to only touch the solid bar and not the wire around it, and jump off these surfaces. This trick is frame perfect, and is nowhere near worth doing if you are new to the game.
12. Use the same buttons that you use to switch back and forth from drill and basic platform to menu between worlds faster. For example, when done with world 1, you can menu to 2-1 with 1 button press this way.

LEVEL SPECIFIC WALKTHROUGH/GUIDE

This will only cover major strats that aren't immediately obvious. Many minor strats exist that are hard to explain in text - watch runs for these. Some minor strats involve learning cycles of levels and responding to the fastest possible cycles. Others are pretty easy to learn from watching runs in general.

1-1 - Intro level, pretty self explanatory. 1-2 - About 3/4 of the way through this level, you can skip some of these loading platforms with either a loading platform manipulation (easier/slower), or a pixel jump (saves about 4-5 seconds over the other strat, MUCH harder). 1-3 - Use the drill to push over one moving block in the last screen as you climb, damage boost through the rest.
1-4 - It is possible to boost jump through some of these switch blocks to either regain platforms or do a minor sequence break (most of the places where this is possible is a very minor time save, though the last section of blocks is notable to skip). Immediately after the checkpoint, it is possible to abuse the long cooldown period of the bulb and go right instead of left. 1-5 - If you can't do the pixel jump yet, there is a more sensible (easier to learn) skip that still saves significant time. Instead of doing the pixel jump, go left from the top part of the elevator and skip the entire bottom portion. 1-6 - Boost jump through this level. Switch to the basic platform to get past the cubes towards the end (they only fly up and stay up long enough for you to pass through if they are undamaged).

2-1 - Drill in this level pretty much destroys it. New patch is about 15 seconds slower in this level because it patches out a bug that allows almost the entire 2nd 1/2 of the level to be skipped. There is a laser warp right before the checkpoint - only stand on unsafe ground on the way to the switch, then hit a laser to warp right next to the elevator. 2-2 - Again, the drill is your friend and allows for faster kills on keys. :) Last segment can be damage boosted through with boost jumping instead of doing the intended method. This is pretty finicky - don't attempt it without at least 3 hearts if you're not fully comfortable with doing this. 2-3 - You can skip the last puzzle area with a high jump from the slingshot. 2-4 - There is a hidden block on the left of the first area (near the yellow tetrahedron) for a developer intended skip. 2-5 - Pretty self explanatory - boost jump up left side, fall down right, activate switch, boost jump up to exit. 2-6 - If you take damage accidentally in the first part of the level, it is faster to set up a death warp. Tt's not worth doing the any% strat here if you have 4 hearts, since that only saves about 1.5 seconds in any% (where you only have 3 hearts) if you set it up perfectly; otherwise it loses time. 2-7 - Fastest fall to the 2nd part of the level is through the left. If you accidentally take damage in the bottom portion and have only 1 heart left, you can death warp after activating the last switch. This is only worth doing if you made mistakes in this level. 2-8 - All the slingshot strats in this level are finicky and require a fair amount of practice. The skip in the first section requires a maximum boost from the slingshot, and a precise weave through the gap in the right. The second skip requires a platform cancel (to hoard 1 additional platform), and a slingshot boost to skip one of the slingshots, followed by using your extra platform to make it over the laser in the end. If you screw up in the second section by not getting a shot out of your slingshot but didn't die, do the rest of the section normally with your hoarded platform (as this saves time over dying).
2-T - Use the drill to cheese this level. There are a few places where it makes sense to damage boost, a not so obvious path about 1/3 of the way through the level (push the block left instead of right), and a pixel jump towards the end if you want to do this level even faster.

3-1 - Minor skip at the very start (go right instead of left), otherwise boost jump through this level. 3-2 - Be very careful with the drill in this level around the fungus enemies, as this level is one of the only ones that is harder in this category than in any%. A few minor skips exist in this level. Before the checkpoint you can go left instead of right to skip the maze (jump from the highest point you can from the platform you made). You can destroy the floor to the next area with the head of your drill (this is finicky). In the final section, you can damage boost and do a pixel jump to skip a few fungi. 3-3 - There's a very minor skip you can do with a peak jump in the start. After the checkpoint, you can skip filling the bucket by just climbing up and going right. This is easier to do than in any% due to extended surf and drill, but still requires a bit of practice to get down the timing and right amount of height out of your jumps to be able to skip the bucket. 3-4 - A few of these sections can be skipped with a peak jump from the bottom right corner to the top left corner. Easiest place to do this is in the room with the blue dropping platforms and the lasers underneath them.
3-5 - Pathing is a bit different from in any%, because it is possible to kill many of the keys through the lasers with the drill since you don't need to be directly above them. Clean boost jumping speeds this level up tremendously. 3-6 - This level is fairly self explanatory. 3-7 - A few places here and there in the first section you can go through faster with the extended surf and jumping as high as you can with 1 platform. You can hoard platforms in the section after the checkpoint from the high ground to skip the rest of the puzzles. Minimum platforms needed to skip everything else is 10 from here with perfect boost jumps and jumping on parts of the level to save platforms, but it's much safer to collect about 16 and boost jump straight up. 3-8 - Fairly self explanatory, boost jump straight up. 3-9 - A few minor skips in the start of the level (can peak jump through the center if you want, and then go under where the fungus is and up from there). Yellow bucket can be skipped entirely. Final puzzle to activate the blue bucket can be skipped by using the drill to push away the block. 3-T - There is a very difficult skip towards the middle of the level (not worth learning if you're new to the game), otherwise this level is self explanatory.

4-1 - There are a couple of damage boosts - one right before the checkpoint, the other right before the end.
4-2 - You can abuse the loading platform by going all the way right (where the orange tetrahedron is hidden), and making sure to not go left more than the very edge of where you need to go to make it past the platform before the green tetrahedron area. If you did it right, the loading platform after the checkpoint should still be loaded. Alternately, it is possible to skip both this plant and the one at the end of the level by mashing platforms extremely fast. 4-3 - There are a couple of laser warps in this level. Only do them if you are 100% comfortable with this level's cycles. 4-4 - Boost jump straight up 4-5 - Several of these boxes and/or maneuvering around them can be skipped with use of extended surf, slingshot boosts, and extended drill. The large section of boxes before the pipe can be skipped, this is very difficult to do and not really worth learning yet if you are new. 4-6 - Fairly self explanatory 4-7 - "" 4-8 - Platform hoarding is faster with the drill than with the laser. Hoard a few platforms right before the checkpoint for early access to the gate, then use the drill to hoard about 13-14 more and boost jump the rest of the level. 4-T - Watch the cycles! This level is pretty difficult casually, and easy to get impatient in. :(

5-1 - A couple of minor laser warps, also watch the behavior of the big bulbs. 5-2 - Takes a bit of practice to not bounce around like an idiot, but you want to always be moving towards the first checkpoint. Cheese the bubbles wherever it makes sense to. Second part of the level, if you only touch bubbles you can laser warp after getting all of the keys. Remember that you can use the drill to kill a key in a way that saves some extra movement. 5-3 - Watch the cycles! Many of these can be boost jumped through much faster than casual strats, which takes separate practice. 5-4 - Since most of these segments have a bubble on the left, and expect you to move counterclockwise to end on the top of a left bubble; you can cheese these types of segments by gaining the platforms you need to jump over them by touching the bubble underneath/to its side. 5-5 - Fastest path is to fall through the middle, weaving around all hazards until you reach the box (kill that key), then go to the checkpoint. Minor death warp after killing that key (DO NOT land on the safe ground that the key is on!). Climb up/left, killing remaining keys on your way. 5-T - PRACTICE THIS LEVEL! It is important to note that the jelly cannons go through everything except for the base of your own platforms (which cancel them). At the start of the level, boost jump up immediately to beat the jelly cannon before it comes out, which makes it significantly easier and faster to do up to the first checkpoint. Ending section can be done faster with a peak jump and loading platform manipulation to reduce side to side movement, but this is difficult to do without dying or falling down. If you are new to the game, focus your practice on not dying over going fast here.

X levels - Boost jump through these. Almost there...

Boss - learn its patterns! Boss fight in this category is easier than any other categories due to having full powerups. Take advantage of your extended drill to space yourself properly from the boss so you can react to things it does and still damage it. Use blocks on the level to protect yourself from the boss's attacks. In the second phase, kill or boost jump away from dangerous enemies like beehives and bulbs. In the third phase, the first 7 hits from the boss are programmed to miss the player unless you try to dodge them.

YAY! You did it! Final length of run is the displayed time during the ending minus the time on the file at the first input you made to enter 1-1. If you are unsure how to do this, ask a mod to help you!