Here is the full list of all 52 Pato Box trophies - there are 42 bronze, 7 silver, 2 gold and 1 platinum.
Defeat Miss Brauch Enten
Full mastery of Pato Box!
Defeat Brauch without getting hit
Destroy only one battery at a time in Brauch's fight
Defeat Kilpatrick at the Casino
Defeat Kilpatrick without getting hit
Interrupt Kilpatrick's headbutt 5 times before defeating him
Defeat Pizzicanatra at the Food Factory
Defeat Pizzicanatra without getting hit
Don't make Pizzicanatra vomit
Defeat Plaganetes at the Laboratory
Defeat Plaganetes without getting hit
Defeat Plaganetes without repeating a phase
Defeat Vorutki at the Sewers
Defeat Vorutki without getting hit
Return all of Vorutki's Bombs.
Defeat Faith at the Penthouse
Defeat Faith without getting hit
Don't let the penthouse boss use the syringe on you
Defeat Mr. Den at the Penthouse
Defeat Mr. Den without getting hit
Defeat Mr. Den at the Heliport
Open the secret door in the lobby
Open all the doors at the living quarters
Win the first prize on the roulette
Finish the Factory without dying
Get ready for business at the office
Find all the rats in the sewers
Find all the patokens in the game
Finish story mode.
Getting answers
Freeze Junior in the laboratory
Find all Patokens at the Lobby
Find all Patokens at the Food Factory
Find all the Patokens at the Casino
Find all Patokens at the Laboratory
Find all Patokens at the Sewers
Find all Patokens at the Offices
Defeat Dark Pato
Defeat Dark Pato without missing a single eye shine
Defeat Dark Pato without getting hit
Finish the Boss Rush in Arcade Mode
Get an S Rank in Brauch's fight in Arcade Mode
Get an S Rank in Vorutki's fight in Arcade Mode
Get an S Rank in Pizzicanatra's fight in Arcade Mode
Get an S Rank in Plaganetes's fight in Arcade Mode
Get an S Rank in Kilpatrick's fight in Arcade Mode
Get an S Rank in Faith's fight in Arcade Mode
Get an S Rank in Dark Pato's fight in Arcade Mode
Get an S Rank in Boss Rush mode in Arcade Mode
Get an S Rank in all fights and modes in Arcade Mode
Defeat all the bosses in Arcade Mode