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 Dr. Schopenstein's replicator
Destroy 25 target boards
Parry 20 enemy attacks
Remove 5 apes with watches from the set
Find 6 missing film reels
Reach the captain of the ghost pirate ship
Find the castaway ape
Defeat the gigantic mutant octopus
Fly through 50 hoops
Max out 3 melee weapons
Destroy all the mutant dinosaur eggs
Defeat the Mechameleon
Destroy 10 target boards
Max out 3 projectile weapons
Kill 3 enemies with parried projectiles
Fly through 20 hoops
Defeat the Mega-Gorilla
Conquer the Nukular ant hive
Kill 3 enemies with one landmine
Kill a large dinosaur with a dagger
Guide 10 enemies into flaming turrets
Kill 10 enemies by jumping on them
Rescue Dick from the Mega-Gorilla