When walking off an object, you are still able to jump in mid-air upto 3/4 of a second after you have walked off the object. This trick is used in the bridge skips on Mansion for example. Get used to how much time you have to walk off the edge, as skips such as Kooky Cook skip and crane skip in Robot Factory require as much distance as possible.

When falling from a decent height where fall damage would be taken, to avoid getting the fall damage animation, which stalls forward movement, hold strafe to cancel this animation. You are able to continue walking forward, however you will still take the fall damage. Holding strafe whilst falling off edges in places where you won't take damage (e.g. the Space Station tunnel) allows you to continue running in the air and moving forward.

In story mode, jump into cut-scene trigger points. After skipping the cut-scene, your character will have moved forward in the cut-scene. This is a way to allow movement in cut-scenes, and can help make certain cycles, and potentially save up to a second. However, one place to avoid this is jumping into the cut-scene in Kooky Carnival after entering the mouth of the clown. A soft lock can be caused by doing this.

Despite being not so great in Modern mode, the slingshot is essential for killing enemies and bosses fast in story mode. Aside from Area 51 and Haunted House, where you need to kill white spy, the slingshot kills him in 4 shots, and general enemies die ridiculously fast from slingshot spam. You can spam the trigger to fire the slingshot as fast as you want, so get used to pressing either R2 or right trigger fast (much harder on Xbox).

Bomb storage for fast death warp: make sure to have a bomb and some trap device (bucket, boxing glove etc) in your inventory. Press and hold the trigger/R2 to start counting the timer down on the bomb. Whilst holding the fire button, press triangle/Y to switch to your trap device. Switch back to the bomb and it will continue counting down by itself. When the timer gets close to one, switch back and complete the actions desired for story mode or whatever. Once completed, switch to your bomb, which will explode (if timed well) very soon after, killing you instantly. The same can be done with dynamite, which takes off full health, or 2 proximity mines, which take off half each.