Here is the full list of all 37 ASTRO BOT Rescue Mission trophies - there are 14 bronze, 19 silver, 3 gold and 1 platinum.
You collected all ASTRO BOT Rescue Mission trophies. You rock! Now, time to get out and see the real world!
Rescued all crew in levels and challenges
Cleared all Challenges fully (obtaining 2 Bots)
Found all Bots in all worlds
Found all Bots in world 5
Got all the toys in the Astro Ship
Blasted the President's name in the credits
Defeated the Alien and completed the game
Found all 4 chameleons in world 5
Defeated the Shark Boss
Cleared 20 Challenges fully (obtaining 2 Bots)
Found all 4 chameleons in world 4
Found all Bots in world 4
Finished off the Spider Boss while looking away
Defeated the Spider Boss
Got half the toys in the Astro Ship
Found a forgotten prize inside the crane machine
Found all 4 chameleons in world 3
Defeated the Bird Boss
Found all Bots in world 3
Defeated 8 enemies with a single spin attack
Found all Bots in world 2
Get Astro stuck to your face underwater
Cleared 10 Challenges fully (obtaining 2 Bots)
Found all 4 chameleons in world 2
Defeated the Octopus Boss
Defeated an enemy by retracting the rope under it
Scored a goal on the beach
Get shocked while splashing water
Splashed yourself with the water gadget
Found all 4 chameleons in world 1
Found all Bots in world 1
Got your first toy in the Astro Ship
Defeated the Gorilla Boss
Hit Astro with the controller in the VR Menu
Cleared your first Challenge fully (obtaining 2 Bots)
Completed the first stage