Here is the full list of all 35 Legendary Edition: Mass Effect trophies - there are 20 bronze, 10 silver, 4 gold and 1 platinum.
ME1: Complete the game on any difficulty
ME1: Complete Ilos
ME1: Complete Virmire
ME1: Use Charm or Intimidate to resolve an impossible situation
ME1: Use medi-gel 50 times
ME1: Complete Feros
ME1: Complete the majority of the game
ME1: Complete 5 missions with the turian squad member
ME1: Land on 8 uncharted worlds
ME1: Complete Noveria
ME1: Find all primary Alien: Council Races, Extinct Races and Non-Council Races codex entries
ME1: Land on 4 uncharted worlds
ME1: Complete 5 missions with the asari squad member
ME1: Complete 5 missions with the Alliance soldier squad member
ME1: Locate Dr. T'soni in the Artemis Tau cluster
ME1: Complete 5 missions with the Alliance sentinel squad member
ME1: Land on an uncharted world
ME1: Become a Spectre
ME1: Complete 5 missions with the krogan squad member
ME1: Complete 5 missions with the quarian squad member
ME1: Complete Eden Prime
ME1: Acquire all trophies
ME1: Use biotic Lift 25 times
ME1: Use biotic Throw 25 times
ME1: Use biotic Warp 25 times
ME1: Use biotic Singularity 25 times
ME1: Use biotic Barrier 25 times
ME1: Use biotic Stasis 25 times
ME1: Use Damping Field 25 times
ME1: Use AI Hacking 25 times
ME1: Use Shield Overload 25 times
ME1: Use Sabotage 25 times
ME1: Use Neural Shock 25 times
ME1: Accumulate 75% of total possible Paragon or Renegade points
ME1: Complete the Bring Down the Sky mission.