We've created a spreadsheet to archive speedruns that have become obsolete as the game has continued to develop and update, including runs from v1.0.1 onward. You can view the spreadsheet with the link below.
https://docs.google.com/spreadsheets/d/1yQIaetT_zp2kgsis86MNAPSFnRgUU7uF6z6ZviFQoQE/edit?usp=sharing
Edit: Tutorial is out of date as of v1.0.1, sorry.
For anybody who's interested in the run and doesn't yet know the route well.
Using a couple upgrades available at the start of the game, it's possible to reach the Ancient Ruins on day 1 of the in-game timer. This run intends to unlock the achievement for visiting the location as quickly as possible (glitchless). If you're not a fan of reading, there's an example/reference run I completed at the end of this post.
To enter the Ancient Ruins, the player is required to obtain 6 plorts: Rock, Tabby, Phosphor, Honey, Boom, and Rad. This run will use jumps to bypass slime doors to eventually obtain one of each plort to open the Ancient Ruins as quickly as possible.
To start the run, a player needs to amass 700 newbucks in total and obtain a slime key. Once done, they can purchase the Jetpack and Power Core upgrades. These will be the only upgrades necessary to reach the Ancient Ruins. Obtaining a pink slime before or shortly after these upgrades will be useful later.
To get to the Indigo Quarry and, resultantly, Rad and Boom Slimes, a close jump can be made from the area to the right of the start of the Dry Reef. [This jump can be seen at 4:47 in the example video posted] After landing the jump, you can use a pink slime from earlier to jump up the ledge and save a few seconds. [A box can also spawn in this location] Once completed, the player needs to vac up at least 1 Boom Slime and 1 Rad Slime before teleporting back to the Ranch through the portal at the end of the Indigo Quarry. It's also necessary to get a Rock Slime before the next step, but they can be obtained easily in the Dry Reef as well.
After obtaining the 3 slimes from the Indigo Quarry, the next stop is the Moss Blanket. You can skip the slime door here with incredible ease using a simple jump from the boardwalk. [This jump can be seen at 7:22 in the example video posted] After entering the Moss Blanket, head to the right and use the slime key from earlier to open the door to the Ancient Ruins entrance. Toss the 3 slimes in here for later.
At this point, the run is almost over. The player just needs to fetch 4 of any fruit, 3 pink plorts, 1 tabby plort, and create a Phosphor-Honey largo slime. Once all of these have been collected, it's time to return to the Ancient Ruins entrance and open the door.
Inventory and slime management is important here so that you don't accidentally create a tarr, so be cautious during the process. Firstly, place the tabby plort in its slot right away to free up some space and then locate the slimes you dropped here earlier. Use the 3 pink plorts to turn them into largos so they can eat the fruit you brought, then feed your 4 pogofruit to each slime. [I would suggest feeding the phosphor-honey first as he can become a tarr the easiest, then shooting him out of the way] Once you've fed and juggled plorts, you should be able to open the Ancient Ruins door. When the achievement pops up on screen, the run is over.
Here is an example/reference run I completed 2 weeks ago with a time of 11:38: