There are 14 Trophies that can be collected.

Bronze

Primitive Discoveries
Collect 5 special bubbles.

Hotfoot It
Complete the race on Hot Stepping with at least 2800 Points left on the clock.

In the Move Groove
Complete the race on Learning to Move with at least 1000 Points left on the clock.

Ace Prehistoric Paradise
Ace Prehistoric Paradise.

Ace Cro-Magnon City
Ace Cro-Magnon City.

Ace Fossil Fight
Ace Fossil Fight.

Pterodactyl Terror
Achieve a score of 4500 in the Primordial Shoot Survival Challenge.

The Hiccups
Achieve a score of 4500 in the Acid Reflux Survival Challenge.

High Flyer
Achieve a score of 5500 in the Pterodactyl Toss Survival Challenge.

Molten Master
Achieve a score of 3500 in the Pyroclastic Flow Survival Challenge.

Extinct
Destroy the T-Rex boss.

Silver

Collect-a-saurus
Collect 15 special bubbles.

Five-a-Day
Ace Inside Big Rex with 5 players.

Gold

Collect-a-saurus Rex
Collect all 25 special bubbles.

http://www.ps3trophies.org/game/sackboys-prehistoric-moves/trophies/