Here is the full list of all 44 LASTFIGHT achievements.
Complete Story mode without transforming into a single Death Dealer
Beat Tomie Sector without using a "Continue"
Complete Story mode (with any character)
Complete Story mode in less than 20 minutes
Avoid using a "Continue" when playing the last level
Unlock Sector
Press "Continue" between 1 and 0 seconds
Land the first blow in every first round of each match in Story mode
Watch all the pins at least once
Find the right pin combination
Complete 100 games in Versus mode
Win a round and keep hold of the trophy for the whole of the next round
Win the right to change the stage 10 times
Pick your buddy up 3 times in the same game
Carry your buddy for 5 seconds in a row in the same round
Send your buddy the third anitrans
Complete five 4-player games in a row
Collect all the pins in Collection mode
Win a match with two perfect rounds
Achieve a play time of 5 hours (not including time in the menus)
Choose a random character and stage and then win the match
Win the game after being one round down and having less than 5% life in the second round
Shoot 50 bullets / torpedoes / missiles
Throw 40 fridges
Block 200 blows
Achieve 20 perfect rounds
Complete 10 matches by throwing an object at your opponent
Destroy all the destructible elements in the game at least once
Use each object / weapon in the game at least once
Break an object thrown at you
Knock out an opponent using only objects
Hit your opponent by throwing an object from the other side of the room
Win a match without using a single special move or object
Play in all stages at least once
Play with all the characters at least 1 time
Complete a match with each of the four transformations
Take a single anitrans and keep it until the end of the round
Don't take any anitrans and win the game
Transform without doing any damage
Transform into a Death Dealer 5 times in the same match
Win five rallies
Hit your opponent with an object after a six-shot rally
Pull off a combo with over 450 damage
Win a match with a double time-out