A standard category where you just need to finish the game as fast as you can, regardless of how many items or heart containers you collect along the way.
The being said, it is very probable that the wall jump or double jump upgrades can't be skipped. But you can certainly finish without collecting all the other items. (I finished my first game with 4/8 heart upgrades and without the triple shot upgrade).
Also, you can add a difficulty variable as subcategory. In the options you can choose for "normal", "hard" and "death" difficulties.
In normal difficulty you start with 4 hearts. In hard difficulty you start with 3 hearts, and there are much more enemies/spikes on screen. Death mode is like hard difficulty, but you don't have hearts at all. So EVERY hit will send you to the latest checkpoint, and hearts containers don't have any effect.
The number of hearts at the beginning is an indicator for the difficulty, and it is also shown at the end in the credits page with all other statistics.