Fast level exit

When sound is enabled, Fox plays a level-ending jingle, and will only continue as soon as no jingle is playing.

Press F3 before exiting a level to disable the music.
Exit the level and split.
Optionally, press F3 to re-enable the music, or continue without sounds.
Press Fire (Space or Return) to dismiss the next level's intro screen.

Bounce and grab

E.g., to pass the level 3 central bottle thrower without carpet or sewers, and still carry the spring past this obstracle. This allows to reuse the same spring elsewhere.

Carry a spring.
Jump vertically.
After the highest point of the jump arc, throw the spring upwards.
Move left or right, to not get bonked by the falling spring.
Jump high, aiming towards above where the spring will land.
During the jump, press and hold Jump (Up), Crouch (Down), Fire (Space or Return).
Land on the rebounding spring while still holding those keys.
The spring will then push you upwards and you will also grab the spring.

Extra-high bounce

E.g., to scale the high wall in level 5 towards the 5-bee pyramid.

Throw a spring upwards.
Bounce-and-grab with the tech above.
Re-throw the spring upwards from the resulting high jump apex.
Bounce a second time off the falling spring.

Stick throwable items into a wall

E.g., to climb towards the ceiling in level 4 with the bowling ball. You cannot merely hold the item into the wall and press Fire; then, the item would slide away from the wall. But there are three methods to make the item stick.

With enemy:

Hold the item inside the wall, holding Crouch (Down).
Let an enemy touch you.

Without anything:

Hold the item inside the wall, holding Crouch (Down).
Press at the very same time Jump (Up) and Fire (Space or Enter).

With throwable item:

Throw a second item upwards in front of the wall.
Grab the item that you want to stick in the wall.
Hold the item inside the wall, holding Crouch (Down).
Get bonked on the head with the falling second item.

The method with the trowable item is a hard legacy method. The TAS used that for the second level 4 ceiling clip. Then gluki found the easier and faster without-anything method to make the second level 4 clip RTA-viable.

Level 4 ceiling clip

Preparation:

Stick the bowling ball into the wall, see above. The slow-walking enemy can help.
Bounce repeatedly on the ball.
You're now standing high on the ball below the ceiling.

To clip through the ceiling, repeat the following cycle at least 3 times:

Keep holding Jump (Up) throughout all following steps.
Crawl away from the wall by pressing Crouch (Down) and Left.
As soon as you fall, release Crouch (Down) and Left.
Immediately hold Right.
Because you have fallen only a few pixels, you should bounce off the ball.
This raises the ball. Repeat this cycle until you have clipped.

Korean Mummy Strat

To kill the mummy boss in level 9 while it's standing still.

Stand slightly further away from the mummy than where you trigger its walk.
While holding Crouch (Down), press Jump (Up) to activate tippy toes.
Enter the mummy's walk trigger area and steal the bowling ball.
Leave the walk trigger area before tippy toes time out.

The Korean Mummy Strat has this flowery name because Simon found it in a Korean Let's Play of Fox.

The tippy toes feature a.k.a. sprite bug is not available when you play with the trainer Moktar the Fox, I tested only MtF version 2.1.1. You may still patch your level codes with MtF to avoid code duplication, but to access tippy toes, you must run the so-patched or unpatched Fox without MtF.

Bonk to fly high

A.k.a. Turbo Jump; this term is used by Jesses. This is a hard method to ascend to the flying platforms at the start of level 11, but the TAS chooses this and gluki also used it in Any% All Levels.

Throw an item upwards.
Stand under the item to have it bonk you on the head.
At the same time as it bonks, let an enemy touch you.

Stacking on the level 11 code lamp

An alternative method if bonking to fly high is too hard.

The crate that you stack on the lamp should be about 1/3 tile widths to either horizontal side of the lamp: Enough so that the crate's center is still above the lamp's square tile, because the crate wouldn't stay on the lamp otherwise, but as far to the side as possible.

Place the spring underneath lamp/crate, carefully aligning it horizontally so that, after you will have bounced on the spring to stick it into the lamp/crate, the spring will end about 1/3 to the other horizontal side of where you stuck the crate.

Carry a second crate with you for the end of the shortcut. Bounce off the spring repeatedly to stick it into the lamp/crate. The horizontal offset between spring and first crate (2/3 of a tile with in total) allows you to land on the spring easily without the first crate in the way.

Fast extra bonus conversion

During a level, press LeftCtrl + LeftAlt + Q to instantly convert extra bonuses into extra lifes. Press Fire to exit the credits screen again. This prevents the time-consuming conversion at the end of a level.