Here is the full list of all 55 Sword Art Online Re: Hollow Fragment trophies - there are 46 bronze, 6 silver, 2 gold and 1 platinum.
Defeat 100 HNM-class monsters in multiplayer.
Complete all galleries.
Take Kirito up to level 200 or higher.
Defeat the boss of the high-difficulty test area.
Clear the game without losing any Assault Team members.
Complete the game with over 100 hours of play time.
Defeat Yuuki.
Defeat the last boss on the 100th floor.
Obtain all last attack bonuses.
Defeat the 99th floor boss.
Defeat the 98th floor boss.
Defeat the 97th floor boss.
Defeat the 96th floor boss.
Reach maximum affinity with Silica.
Reach maximum affinity with all heroines.
Reach maximum affinity with Leafa.
Defeat the 95th floor boss.
Defeat the 94th floor boss.
Defeat the 93rd floor boss.
Defeat the 92nd floor boss.
Defeat the 91st floor boss.
Defeat the 90th floor boss.
Clear a set number of elements on the Implementation List.
Reach maximum affinity with Asuna.
Reach maximum affinity with Sinon.
Clear a set number of Hollow Missions.
Defeat Hollow Kirito.
Defeat the Administration Area boss.
Defeat the Alevaste Otherworld boss.
Defeat the Driogeer Skycaves boss.
Defeat PoH.
Defeat the Graceleaf Bay boss.
Defeat the Bastia Gate boss.
Reach maximum affinity with Philia.
Defeat the 89th floor boss.
Defeat the 88th floor boss.
Defeat the 87th floor boss.
Defeat the 86th floor boss.
Defeat the 85th floor boss.
Defeat the 84th floor boss.
Defeat the 83rd floor boss.
Defeat the 82nd floor boss.
Earn a hundred million Col.
Reach maximum affinity with Lisbeth.
Participate in multiplayer games for over 20 hours.
Defeat the 81st floor boss.
Defeat the 80th floor boss.
Defeat the 79th floor boss.
Defeat the 78th floor boss.
Defeat the Selvendys Forest boss.
Defeat the 77th floor boss.
Defeat the 76th floor boss.
Clear the tutorial.
Obtain all trophies.
Successfully enhance a weapon 200 times.