Here is the full list of all 47 Digimon All-Star Rumble trophies - there are 38 bronze, 4 silver, 4 gold and 1 platinum.
Unlocked all Trophies.
Completed the entire set of DigiCards.
50 hours or more total play time achieved.
250000 or more total Bits gained achieved.
Collected 100 or more DigiCards.
Fight on Lava Pit in Battle Mode, 10 or more times.
Fight on Digital Station in Battle Mode, 10 or more times.
Used Impmon in Battle Mode 20 or more times.
Fight on Proton Shrine in Battle Mode, 10 or more times.
Used Guilmon in Battle Mode 20 or more times.
Fight on Tilly Valley in Battle Mode, 10 or more times.
Play Bomb Battle in Battle Mode, 10 or more times.
Used Wormmon in Battle Mode 20 or more times.
Fight on Coela Beach in Battle Mode, 10 or more times.
Used Veemon in Battle Mode 20 or more times.
Play Flag Battle in Battle Mode, 10 or more times.
Used Gatomon in Battle Mode 20 or more times.
Fight on Native Forest in Battle Mode, 10 or more times.
Used Gomamon in Battle Mode 20 or more times.
Play Damage Race in Battle Mode, 10 or more times.
Fight on Toy Town in Battle Mode, 10 or more times.
Used Tentomon in Battle Mode 20 or more times.
Fight on King's Castle in Battle Mode, 10 or more times.
Play Medal Battle in Battle Mode, 10 or more times.
Fight on Factory Town in Battle Mode, 10 or more times.
Used Biyomon in Battle Mode 20 or more times.
Play Point Battle in Battle Mode, 10 or more times.
Used Gabumon in Battle Mode 20 or more times.
Fight on Digital Plains in Battle Mode, 10 or more times.
Used Agumon in Battle Mode 20 or more times.
Cleared Story mode with all characters.
Collected 50 or more DigiCards.
50000 or more total Bits gained achieved.
10 hours or more total play time achieved.
5 hours or more total play time achieved.
10000 or more total Bits gained achieved.
Cleared Story mode.
Cleared the Story mode stage, Coela Beach.
Cleared the Story mode stage, King's Castle.
Cleared the Story mode stage, Native Forest.
Cleared the Story mode stage, Digital Station.
Cleared the Story mode stage, Factory Town.
Cleared the Story mode stage, Proton Shrine.
Cleared the Story mode stage, Digital Plains.
Used Shoutmon in Battle Mode 20 or more times.
Used Dorulumon in Battle Mode 20 or more times.
Play Survival in Battle Mode, 10 or more times.