Note that your v1.1 save carries over and you do not need to beat levels in the April Fools build.
There’s one main requirement: your rank on every level. If you don’t care about the technical details, getting at least a B on every level (not including Arenas or Death Mode) will suffice.
Unlocking CToP works off of a “points” system. Your rank on a level gives points, and your total score is what determines if CToP is unlocked. P is 5, S is 4, A is 3, B is 2, C is 1, and D is 0. An uncleared level counts as negative 4. To unlock CToP, you need at least 40 points total across all the main levels, not including Arenas or Death Mode. Once you meet the requirement, it can be accessed on the Top Floor by going through the door to the right of the Arena.