Here is the full list of all 39 Jupiter & Mars trophies - there are 22 bronze, 12 silver, 4 gold and 1 platinum.
Unlock All Trophies
Be swept away by the ocean current
Rescue the whale calf in Clocktower
Meet an Elder.
Reunite with Mars.
Watch the whale clear a path for you in Realm of Poseidon.
Watch to the end of the final cutscene.
Complete your first treasure set.
Find 15 treasures.
Find all the treasures.
Find all the treasures in Sunpool.
Find all the treasures in Clocktower.
Find all the treasures in Plastic Beach.
Find all the treasures in Realm of Poseidon.
Find all the treasures in A.T.L.A.N.T.I.S.
Rescue the turtles in Sunpool.
Rescue the manta rays in Sunpool.
Rescue the pufferfish in Clocktower.
Rescue the pufferfish in Sunpool.
Rescue the conches in Plastic Beach.
Rescue the crabs in Sunpool.
Rescue the crabs in Realm of Poseidon.
Rescue the manta rays in A.T.L.A.N.T.I.S.
Free the ethereal dolphin pod.
Rescue all the mako sharks.
Rescue every creature.
Shut down the Space Station in Sunpool.
Shut down the Space Station in Clocktower.
Shut down the Space Station in Plastic Beach.
Shut down the Space Station in Realm of Poseidon.
Shut down the Space Station in A.T.L.A.N.T.I.S.
Shut down all the AHDs.
Unlock the Tail Kick powerup.
Unlock the Aqualung powerup.
Unlock the Submariner powerup.
Unlock the Blubber powerup.
Unlock the Conch powerup.
Break 50 objects with Mars' conch shell.
Start a new journey with Rocket.