Here is the full list of all 128 BATTLETECH achievements.
Completed a Campaign with Iron Man enabled
Have a 'Mech and its Pilot survive being knocked down, shutdown, and shot in the head
Become Allied with House Marik
Become Allied with House Liao
Retreated 10 times from a contract before any of your 'Mechs got destroyed
Hired 100 MechWarriors
Hired 50 MechWarriors
Hired 25 MechWarriors
Watched all of the credits
Crowned a rightful ruler
Invaded a capital
Fielded a lance of four King Crabs, won, and lost no 'Mechs
Acquired all 36 launch date 'Mechs
Hired five MechWarriors
Liberated the world of Tyrlon
Learned an important secret
Liberated the world of Itrom
Discovered ancient technology
Destroyed an enemy light 'Mech with a Highlander Death from Above
Captured a villain
Liberated the world of Smithon
Fielded a lance of four UrbanMechs, won, and lost no 'Mechs
Destroyed an UrbanMech with Flamers
Destroyed an enemy Orion with an AC/20 headshot
Destroyed 50 enemy vehicles with melee
Saved up over 20 million C-bills
Purchased a new 'Mech chassis
Destroyed an enemy 'Mech with Death from Above using an UrbanMech
Completed 100 mercenary contracts
Liberated the world of Panzyr
Refitted a 'Mech other than an Awesome equipped with three or more PPCs
Started a war
Won a skirmish match with an Atlas vs four AI Commandos
Won a skirmish match with three Commandos vs an AI Atlas
Won 100 online matches
Retreated once from a contract before any of your 'Mechs got destroyed
Won a 4v4 match with all of your 'Mechs being Locusts
Won 50 online matches
Played 100 online multiplayer matches
Won 25 online matches
Played 50 online multiplayer matches
Lost 10 online matches
Ejected 20 times
Played 5 online multiplayer matches
Won a match with three 'Mechs vs. an OpFor with four 'Mechs
Won an online multiplayer match
Battled someone who has this achievement (and therefore has either battled HBS developer/BT tourney champ Chris Eck or battled someone who battled someone...who has)
Won 100 skirmish matches
Destroyed 500 'Mechs
Destroyed 50 heavy 'Mechs
Destroyed 50 assault 'Mechs
Ejected 5 times
Won 50 skirmish matches
Destroyed 20 enemy 'Mechs with Death from Above
Destroyed an enemy 'Mech and your own 'Mech while using Death from Above
Destroyed 5 enemy 'Mechs with Death from Above
Won a skirmish match with a Lance Value 15m less than the OpFor's
Your light 'Mech killed an assault 'Mech with a melee attack
Won a skirmish match with a Lance Value 10m less than the OpFor's
Won a skirmish match with a Lance Value 5m less than the OpFor's
Won 10 skirmish matches
Won a skirmish match using fewer 'Mechs than the AI opponent
Won a skirmish match with more than 25m Lance Value on both sides
Won a skirmish match at the War (25m) Lance Value Budget
Won a skirmish match at the Battle (20m) Lance Value Budget
Lost to the AI one time
Maxed out a MechWarrior's Piloting stat
Won a skirmish match at the Clash (15m) Lance Value Budget
Maxed out a MechWarrior's Guts stat
Maxed out a MechWarrior's Tactics stat
Saved up over 10 million C-bills
Destroyed 50 medium 'Mechs
Destroyed an enemy 'Mech's head with a Called Shot
Destroyed 250 'Mechs
Completed a contract with one mech remaining and no pilots killed
Saved up over 5 million C-bills
Destroyed 50 enemy 'Mechs in melee
Completed 50 mercenary contracts
Maxed out a MechWarrior's Gunnery stat
Refitted 50 'Mechs
Your pilot ignored the safety instructions and destroyed their 'Mech by overheating while firing weapons
Destroyed an enemy 'Mech with Flamers
Built 10 'Mechs by collecting/salvaging their parts
Destroyed two 'Mechs in the same turn using Multi-Target
Completed 25 'Mech repair work orders
Completed 25 mercenary contracts
Refitted a 'Mech with only Missile weapons
Destroyed 50 light 'Mechs
Refitted 25 'Mechs
Refitted a 'Mech with only Energy weapons
Destroyed 50 'Mechs
Killed a Pilot without destroying their 'Mech
Negotiated for nothing but salvage in a completed contract
Successfully completed a contract using only one 'Mech
Negotiated for nothing but reputation in a completed contract
Missed a Called Shot
Refitted a 'Mech with only Ballistic weapons
Recovered an ancient ship
Destroyed 5 enemy 'Mechs in melee
Refitted a 'Mech with only Support weapons
Completed 10 mercenary contracts
Removed both arms and one leg from an enemy 'Mech
Destroyed 5 enemy vehicles with melee
Destroyed an enemy 'Mech's leg with a Called Shot
Made a melee attack on an enemy 'Mech that was knocked prone
Completed your first mercenary contract
Refitted a 'Mech with the maximum amount of armor
Removed both arms from an enemy 'Mech
Suffered a terrible betrayal
Removed all the limbs of an enemy 'Mech
Destroyed an enemy 'Mech with an Alpha Strike
Removed one arm from an enemy 'Mech
Established a history
Start a campaign with 'Mechs requiring 8 parts, then complete 10 'Mechs
Become Allied with House Steiner
Become Allied with House Davion
Become Allied with House Kurita
Become Allied with the Magistracy of Canopus
Become Allied with the Taurian Concordat
Completed your first Career Mode campaign with any rank
Accomplished a Career Mode score at Veteran rank (>320,000 points)
Accomplished a Career Mode score at Elite rank (>480,000 points)
Accomplished a Career Mode score at Legendary rank (>720,000 points)
Completed Career Mode with Iron Man enabled