Here is the full list of all 127 Mass Effect Legendary Edition achievements worth 2,915 gamerscore.
ME3: Set 100 enemies on fire with powers
Finish Mass Effect 1, 2 and 3 with the same character
ME3: Mission accomplished
ME3: Make the final assault
ME3: Defeat an old adversary
ME3: Stop an out-of-control scheme before it's too late
ME3: Send a warning across the galaxy
Establish or rekindle a romantic relationship in two games in Mass Effect Legendary Edition
ME3: Extract ancient technology
ME3: Deliver most of the Galaxy at War assets to the final conflict
ME3: Call down an orbital strike
ME3: Disable a group of fighter squadrons
ME3: Sabotage a dreadnought
ME3: Evacuate a scientific facility
ME3: Discover an enemy's monstrous origin
ME3: Win a political stand-off
ME3: Explore a lost city
ME3: Survive the swarm
ME3: Obtain two non-customizable suits of armor
ME3: Destroy an Atlas dropped from orbit
ME3: Stop a Cerberus kidnapping
ME3: Dispatch 10 probes to retrieve people or resources in Reaper territory
ME3: Free Omega from Cerberus Occupation
ME3: Hijack an Atlas mech
ME3: Uncover an ancient secret
ME3: Kill a brute while it's charging you
ME3: Defeat a harvester
Kill 2,000 enemies in Mass Effect 1, 2 or 3
ME3: Escape a Reaper in the galaxy map
ME3: Bring a veteran officer aboard
ME3: Modify a weapon
ME3: Visit a store on the Citadel
ME3: Chase down an assassin
ME3: Return to active duty
ME3: Evolve any of your powers to rank 6
ME2: Keep your team alive through the suicide mission
ME2: Save humanity throughout the galaxy from certain annihilation
ME2: Survive suicide mission
ME2: Use the Omega 4 Relay
Establish a romantic relationship in Mass Effect 1, 2 or 3
ME2: Hack a geth collective
ME2: Obtain geth technology
ME2: Confront the Shadow Broker
ME2: Gain the loyalty of the biotic Convict
ME2: Gain the loyalty of the quarian
ME2: Gain the loyalty of the krogan
ME2: Thresher Maw defeated
ME2: Fully upgrade a weapon
ME2: Help the Justicar resolve her mission
ME2: Gain the loyalty of the Assassin
ME2: Gain the loyalty of Archangel
ME2: Gain the loyalty of the Professor
ME2: Successfully recruit the Justicar
ME2: Complete the investigation of a derelict alien vessel
ME2: Successfully recruit the quarian
Kill 1,000 enemies in Mass Effect 1, 2 or 3
ME2: Successfully recruit the Assassin
ME2: Gain the loyalty of the Cerberus Officer
ME2: Gain the loyalty of the Cerberus Operative
ME2: Evolve any power
ME2: Defend a human colony from attack
ME2: Successfully recruit the biotic Convict
ME2: Successfully recruit the krogan
ME2: Visit 100% of the planets in an unexplored cluster
ME2: Gain the loyalty of the mercenary
ME2: Gain the loyalty of the thief
ME2: Complete 5 missions discovered by scanning unexplored worlds
ME2: Successfully shut down the rogue VI in Project Overlord
ME2: Perform 30 headshot kills with any weapon on humanoid targets
ME2: Complete a mission discovered by scanning an unexplored world
ME2: Successfully recruit Archangel
ME2: Make 20 enemies scream as they fall or are set on fire
ME2: Unlock 15 new Mass Effect 2 codex entries
ME2: Complete any research project in the Normandy's laboratory
ME2: Successfully recruit the Professor
ME2: Return to active duty
ME2: Save your crew from an overwhelming attack
ME1: Complete the game on any difficulty
ME1: Complete Ilos
Kill 250 enemies in Mass Effect 1, 2 or 3
ME1: Use biotic Stasis 25 times
ME1: Complete the majority of the game
ME1: Complete the Bring Down the Sky mission.
ME1: Complete Virmire
ME1: Use biotic Singularity 25 times
ME1: Use medi-gel 50 times
ME1: Use biotic Barrier 25 times
ME1: Use AI Hacking 25 times
ME1: Use Charm or Intimidate to resolve an impossible situation
ME1: Use biotic Warp 25 times
ME1: Complete Feros
ME1: Accumulate 75% of total possible Paragon or Renegade points
ME1: Use biotic Lift 25 times
ME1: Use biotic Throw 25 times
ME1: Complete Noveria
ME1: Use Damping Field 25 times
ME1: Use Shield Overload 25 times
ME1: Complete 5 missions with the asari squad member
ME1: Locate Dr. T'soni in the Artemis Tau cluster
ME1: Use Sabotage 25 times
ME1: Complete 5 missions with the quarian squad member
ME1: Land on 8 uncharted worlds
ME1: Complete 5 missions with the Alliance soldier squad member
ME1: Land on 4 uncharted worlds
ME1: Complete 5 missions with the krogan squad member
ME1: Land on an uncharted world
ME1: Find all primary Alien: Council Races, Extinct Races and Non-Council Races codex entries
ME1: Become a Spectre
ME1: Complete 5 missions with the turian squad member
ME1: Complete 5 missions with the Alliance sentinel squad member
ME1: Complete Eden Prime
ME1: Use Neural Shock 25 times
ME2: Incinerate the armor of 25 enemies
ME2: Disrupt the shields of 25 enemies
ME2: Hit 20 different targets with multiple biotic powers to combine the effects
ME2: Warp the barriers of 25 enemies
ME3: Perform any combination of 50 biotic combos or tech bursts
ME3: Overload the shields of 100 enemies
ME3: Lift 100 enemies off the ground with powers
ME3: Kill 10 guardians with headshots from the front while their shields are raised
ME3: Upgrade any weapon to level 10
ME3: Defeat a group of Spectre-level opponents on Normal, Hardcore, or Insanity
Complete Mass Effect 1, 2 or 3 on Insanity without changing difficulty
Complete two games in Mass Effect Legendary Edition on Insanity without changing difficulty
Complete all three games in Mass Effect Legendary Edition on Insanity without changing difficulty
Establish or rekindle a romantic relationship in all three games in Mass Effect Legendary Edition
Kill 100 enemies with melee attacks in Mass Effect 1, 2 or 3