It can only be accessed via Level 11: Dino Might!
But first, several steps are required.
Step 1: Earn 10 Relics (any value, doesn’t matter if Sapphire, Gold or Platinum). Relics are rewards for beating best times in speedruns. After beating a level for the first time you can pick up a stopwatch at the start of the level and do the speedrun. Getting 10 Relics unlocks Level 27 in the secret warp room. While in the center of the Warp Area (from where you select levels) stand on the orange button in the middle. It will bring you to the basement where level 27 can be started.
Step 2: Play Level 27 “Hang’ Em High” and pick up the Yellow Colored Gem at the end. You’ll walk right into it, would be hard to miss. Complete the level afterwards to make it count.
Step 3: Start Level 11 “Dino Might!” (Warp Room 3). About one minute into the level before the dinosaur egg you can activate the yellow gem path. This is why we needed the yellow gem, because without it you only see the outlines of the platform and cannot activate it.
Step 4: The secret exit is found on this yellow gem path. Keep playing until the big dinosaur chases after you. At the start of the dinosaur chase there are two pterodactyls (flying dinosaurs) sitting on tree trunks. Jump onto the second one to trigger the secret exit — trophy unlocked!
A video guide of all the steps described above, showing the secret entrance to Eggipus Rex
If you want to repeat the level you must use the yellow gem path again and hang on to the pterodactylus. However, if you lose all lives you can simply choose to continue and repeat it as often as you want.
Want more secrets? Check out the second secret level in the game called “Hot Coco“.