Here is the full list of all 26 Lab Remnants achievements.
Spend 70 coins or more in a single run
Finish a run with 100 coins or more
Finish a run with 300 coins or more
Finish a run with 500 coins or more
Defeat it
Defeat it on master mode
Make a deal
Make two deals in a single run
Make three deals in a single run
Upgrade one character
Fully upgrade one character
Fully upgrade every character