Is it possible to see Hot Coco and Eggipus Rex leaderboards?
Unfortunately, it doesn't look like it's possible. I have yet to find a way to view these, and it appears that others (1, 2) have yet to find this information as well, such as in this thread:
No, it's not possible. Write it down on a piece of paper or try to remember it. You can only access Eggipus Rex from the gem path in Dino Might when you're near the second pterodactyl, and you can only access Hot Coco by hitting the alien sign in Road Crash. You can't see any progress-so-far anywhere.