When you already accessed the higher jump from the first Boss, you can do a higher jump by holding L1 + L2 + R1 + R2 and pressing X(2). You should jump slightly higher. Note: This is very useful when getting the five extra lives by jumping over the Yellow Gem Ride.

Hold Circle or L1 and press X, then X again when in mid-air. You will jump slightly higher because Crash crouches before his jump. Note: You cannot run and do this because you will slide.