Here is the full list of all 54 Sword Art Online: Hollow Fragment trophies - there are 44 bronze, 7 silver, 2 gold and 1 platinum.
Complete the game without any one of the Assault Team dying
Complete the game after 100 hours of playing time
Defeat Yuuki
Defeat the final boss in floor 100
Defeat the boss in floor 99
Raise your bond with Silica to the max level
Raise your bond with all heroines to the max level
Defeat the boss in floor 98
Raise your bond with Lisbeth to the max level
Defeat the boss in floor 97
Raise your bond with Leafa to the max level
Defeat the boss in floor 96
Total multiplayer time exceeds 20 hours
Raise your bond with Sinon to the max level
Defeat the boss in floor 95
Raise your bond with Philia to the max level
Defeat the boss in floor 94
Raise your bond with Asuna to the max level
Defeat the boss in floor 93
Defeat the boss in floor 92
Defeat the boss in floor 91
Defeat the boss in floor 90
Defeat Hollow Kirito
Defeat the boss in floor 89
Defeat the boss in floor 88
Defeat the boss in floor 87
Defeat the boss in floor 86
Defeat the boss in floor 85
Defeat the boss in floor 84
Defeat the boss in floor 83
Defeat the boss in floor 82
Defeat the boss in floor 81
Defeat the boss in floor 80
Defeat the boss in floor 79
Defeat the boss in floor 78
Defeat the boss in floor 77
Defeat the boss in floor 76
Defeat the boss of the Control Area
Defeat the boss of the Otherworld Area
Defeat PoH
Defeat the boss of the Great Void Area
Defeat the boss of the Cove Area
Defeat the boss of the Floating Ruins Area
Defeat the boss of the Sea of Trees Area
Complete tutorial
Collect all trophies
Get every Last Attacking Bonus
Complete more Hollow Missions than required
Complete more Implement Element Researches than required
Upgrade weapons 200 times
Find all collectibles for the gallery
Kirito reaches at least level 150
Save 100 million Col
In a multiplayer game, defeat at least 100 level HNM creatures