There are bonus rounds in each stage of Gex except Rez Knight Fever. Here's how to find them:

CEMETARY:
Play through the level unti you reach the camera. Climb up the wall to the left (with a few spikes). look for the floating platform to theright. Jump onto the platform, and keep going right until you reach the bonus portal on the last platform.

NEW TOONLAND:
Climb up the level until you reach the camera with the remote control directly above it. Climb up the remote pedastal. You should see a green block to the left. Jump across the block, then run and fall to the left (DON't JUMP!). Look for the arrow of golden bugs pointing down at the small ledge with the bonus portal.

JUNGLE ISLE:
Walk past the first camera and drop through the collapsing section of the bridge. Swim left through the water and keep moving left into the wall. You can't see the bonus portal, but you can hear it.

KUNG FUVILLE:
Play through the level until you reach the third camera. Go to the right until you reach some steps with a sumo wrestler on the right and a flying eyeball to the left. Do a super-spring jump off the eyeball and bounce up and left to the platform with the bonus portal.

REZOPOLIS:
Play through the level to the second camera. Go to the right until you need to climb upward. Scurry to the top and bounce left across the acid bubbles to the ledge with the bonus portal. You don't even need tobounce on the bubbles, if you jump far enough to the left.