Here is the full list of all 56 Mega Man Battle Network Legacy Collection Vol. 1 achievements.
Complete Mega Man Battle Network 1, 2, and 3.
Complete Mega Man Battle Network 3 Blue.
Activate MegaMan's Humor for the first time in Mega Man Battle Network 3.
Defeat BowlMan in Mega Man Battle Network 3.
Use the chip trader special 30 times.
Receive the extra folder from Folder Boy in Mega Man Battle Network 3.
Complete the "CyberSimon Says" minigame in Mega Man Battle Network 3.
Use Shadow Style in Mega Man Battle Network 3 Blue.
Defeat Punk in Mega Man Battle Network 3 Blue.
Defeat MetalMan in Mega Man Battle Network 3.
Complete Mega Man Battle Network 2.
Use Shield Style in Mega Man Battle Network 2 or Mega Man Battle Network 3.
Defeat SnakeMan in Mega Man Battle Network 2.
Defeat ThunderMan in Mega Man Battle Network 2.
Complete the "Need a Cupid" Request in Mega Man Battle Network 2.
Complete the "Paying in advance" Request in Mega Man Battle Network 2.
Use Guts Style in Mega Man Battle Network 2 or Mega Man Battle Network 3.
Jack in more than 100 times.
Defeat GateMan in Mega Man Battle Network 2.
Defeat ToadMan in Mega Man Battle Network 2.
Complete Mega Man Battle Network.
Repair a defunct vending machine in Mega Man Battle Network.
Defeat ProtoMan in Mega Man Battle Network.
Defeat SharkMan in Mega Man Battle Network.
Defeat SkullMan in Mega Man Battle Network.
Find and return a lost set of dentures in Mega Man Battle Network.
Defeat WoodMan in Mega Man Battle Network.
Earn your first S rank in an in-game battle.
Use a Download Chip for the first time.
Take part in more than 100 battles.
Successfully activate a Program Advance.
Use the Music Player to listen to one or more songs from each game.
Use the chip trader 30 times.
Use Custom Style in Mega Man Battle Network 2 or Mega Man Battle Network 3.
Use Team Style in Mega Man Battle Network 2 or Mega Man Battle Network 3.
Use Ground Style in Mega Man Battle Network 3 White.
Use Bug Style in Mega Man Battle Network 3.
Acquire all addresses in Mega Man Battle Network.
Acquire all chips (including Download Chips) in Mega Man Battle Network.
Correctly answer all of the Quiz Master's questions in Mega Man Battle Network.
Find money that was stolen from a bank account in Mega Man Battle Network.
Correctly answer all of the Quiz King's questions in Mega Man Battle Network 2.
Obtain the S-License in Mega Man Battle Network 2.
Complete the "Help research" Request in Mega Man Battle Network 2.
Complete the "Please help" Request in Mega Man Battle Network 2.
Complete the "Return my gem!" Request in Mega Man Battle Network 2.
Correctly answer all of the Quiz King's questions in Mega Man Battle Network 3.
Complete Mega Man Battle Network 3 White.
Complete the "Help with a will" Request in Mega Man Battle Network 3.
Complete the "Give your support!" Request in Mega Man Battle Network 3.
Complete the "Hide and seek!" Request in Mega Man Battle Network 3.
Complete the "Legendary Tomes" Request in Mega Man Battle Network 3.
Feed a virus for the first time in Mega Man Battle Network 3.
Acquire an SP Virus in Mega Man Battle Network 3.
Defeat MistMan in Mega Man Battle Network 3.
In Mega Man Battle Network 3, visit the BugFrag trader 20 times.