Skip First Level
You can avoid playing the first level if you skip the first cutscene. Skipping the first cutscene will instead take you straight to the first Warp Room.
Revive Crash Bandicoot
If you keep holding Up + Circle after you lose a life Crash will start moving again.
Voodoo Mask
If during a warp tunnel you press X(2), then hold X + Up and release the buttons Crash Bandicoot will receive a voodoo mask after his next life is lost.
Revisit Boss Stages
If you stand on the middle platform of a warp room and then hold L1 + R1 + L2 + R2 + Triangle and press Up when Crash points up or down you will fight the boss of that Warp Room. You only can return to Bosses you have previously encountered.