Here is the full list of all 40 Patapon 2 Remastered trophies - there are 29 bronze, 5 silver, 5 gold and 1 platinum.
Unlock all trophies.
Perform the Brimstone Juju.
Perform the Miracle of the Blizzard.
Perform the Duck 'n' Cover Juju.
Perform the Earthquake Miracle.
Perform the Rain Miracle.
Perform the Storm Miracle.
Perform the Tailwind Miracle.
Complete Level 3 of Fah Zakpon's minigame.
Complete Level 3 of Kon Kimpon's minigame.
Complete Level 3 of Pan the Pakapon's minigame.
Complete Level 3 of Rah Gashapon's minigame.
Complete Level 3 of Shuraba Yapon's minigame.
Complete Level 3 of Ton Kampon's minigame.
Play Tsun Tunpon and Tsuku Tsukupon's minigame for the first time.
Acquire a Babassa rarepon.
Acquire a Mogyugyu rarepon.
Acquire a Wagyanba rarepon.
Beat the game for the first time.
Raise a rarepon to Level 10.
Perform 15 consecutive songs while in Fever mode.
Acquire a Divine Weapon.
Acquire a Demon Weapon.
Defeat a Level 5 boss without losing any troops.
Acquire all 4 drums.
Find a Wep and receive it's rewards.
Perform 5 different songs during one mission.
Unlock every memory in the Yaripon Evolution Map.
Unlock every memory in the Tatepon Evolution Map.
Unlock every memory in the Yumipon Evolution Map.
Defeat Dodonga.
Defeat Mochichichi.
Defeat Centura.
Defeat Manboth.
Defeat Garuru.
Defeat Fennichi.
Defeat Zaknel.
Defeat Shookle.
Defeat Kanogias.
Defeat Dettankarmen.