If you want to complete a few sub objectives, or objectives you will need BL2 to reference the number of requirements. Once you've found the mission you want to edit look to Status and change the mission to ReadyToTurnIn if you want to instantly complete the mission. There are two ways to look for the quest you REALLY want to edit, #1 is looking to mission on the right this will show you the name or 'Codename' of the mission, and #2 is seeing if the mission is Active, Not Started, or Failed. Once you're in your quest information you will notice a lot of quests. Once you've clicked one of these navigate your way to the MissionData collection arrow. Depending on what playthrough you're on, choose from 1 of 2 existing options available since Playthrough 3 has no data yet. Now that you've opened up the collections list you will notice 3 MissionPlaythroughData the first one is Playthrough 1 (Normal Mode), the second one is Playthrough 2 (True Vault Hunter Mode), and the third one is most likely the 'Something Interesting thing' that Gearbox Is planning on when they raise the level cap which will be a Playthrough 3 no doubt. Image below will give assistance if needed.

When you find, it navigate your way to the arrow that will open up the collection window.

Now scroll down until you see MissionPlaythroughs. Firstly you will need to open your save into Gibbed's Borderlands 2 save editor and move your way to 'Raw' to edit your characters Raw Data.

Gibbed save editor for borderlands 2