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