Here is the full list of all 51 Monster Monpiece trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
10 successful First Crush ♡ rubs!
First successful First Crush ♡ rub!
Triggered extreme love!
Ginuma area cleared!
Performed First Crush ♡ rub!
Won 10 offline battles!
Kunaguva area cleared!
Performed fusion for first time!
Trained for the first time!
Acquired a card for first time!
Won a card battle with 0 damage!
Won a card battle for the first time!
Attacked castle for first time!
Battled for the first time!
Started the game for the first time!
Obtained all the trophies!
Hollowlo area cleared!
Ho Kaido area cleared!
Ki Outo area cleared!
Fukuruko area cleared!
Okinava area cleared!
Tokio area cleared!
Si Ku Ork area cleared!
Completed 3 master rings!
Got 100 kinds of cards!
Got 500 kinds of cards!
50 successful First Crush ♡ rubs!
100 successful First Crush ♡ rubs!
Irresistible Force
Triggered extreme love 20 times!
Triggered extreme love 50 times!
Won 30 offline battles!
Won 50 offline battles!
Won 70 offline battles!
Won 100 offline battles!
Partook in your first online battle!
Won 10 online battles!
Won 30 online battles!
Won 50 online battles!
Won 70 online battles!
Suffered your first online defeat
Won 3 online battles in a row!
Won 7 online battles in a row!
Completed 20 master rings!
Cleared the game!
Your Rub P stock has exceeded 10000!
Won 90 online battles!
Triggered extreme love 100 times!
Won 10 online battles in a row!
300 successful First Crush ♡ rubs!
Won 100 online battles!