Here is the full list of all 24 The Deadly Tower of Monsters trophies - there are 10 bronze, 6 silver, 7 gold and 1 platinum.
Complete all other missions
Destroy 25 target boards
Destroy Dr. Schopenstein's replicator
Find 6 missing film reels
Fly through 50 hoops
Defeat the gigantic mutant octopus
Reach the captain of the ghost pirate ship
Find the castaway ape
Remove 5 apes with watches from the set
Destroy all the mutant dinosaur eggs
Defeat the Mechameleon
Max out 3 projectile weapons
Destroy 10 target boards
Max out 3 melee weapons
Fly through 20 hoops
Defeat the Mega-Gorilla
Kill 3 enemies with parried projectiles
Conquer the Nukular ant hive
Guide 10 enemies into flaming turrets
Kill 3 enemies with one landmine
Kill a large dinosaur with a dagger
Parry 20 enemy attacks
Kill 10 enemies by jumping on them
Rescue Dick from the Mega-Gorilla