The Resolution Achievement requires essentially a pacifist playthrough of the game, and is achieved by defeating Alibii Omega while killing less than 10 enemies, as well as not killing any bosses except for ones that must be fought to progress.

Step-by-Step Guide:

-Get Stardust in the Phantom Pit, then backtrack through the forest. Don't enter Mechanical Mine, or fight Blue.

-Go to the Sunken City and complete God's puzzle.

-Go to the Fallen City and complete the Fallen King's puzzle.

-Use the Vile Ritual to go back to the Phantom Pit, then enter Mechanical Mine and complete Marty & Bolshie's puzzle.

-Return to the Plains and enter the Red Plains.

-Defeat Alibii Omega and complete the game.