Firstly, you'll need the Yellow Gem. You can obtain this after collecting 10 Time Trial Relics (any colour). Go to the centre of the Time Twister (Hub world) and take the platform down. Select Level 27 Hang 'em High. The Yellow Gem will be near the end of the level.
Next, go to Level 11 Dino Might! Just after the first checkpoint you'll see a yellow platform. Hop on the platform and follow the route to the Triceratops run. Run down the path and let the second Pterodactyl (it's on the left of the screen) catch you by running into it. It will then drop you into the secret level Eggipus Rex and the trophy will also unlock.
Note: Make sure that you don't have a Mask, otherwise the Pterodactyl won't pick you up.