-( Story related, cannot be missed )-
The final part of the final case is actually rather short, as the rest of this case has been. This is a story-related achievement so you can't complete the game and not get this. However, should you still want some help, go ahead and check out the spoiler tag below.
*** Spoiler - click to reveal ***Act 5: Album (Re)Cover
Part 3a: Flame Princess on Keys
Marceline will tell you that you've got two members left to get, and that PB is in distress over something. After finishing your talk, talk to PB to find that she's missing some outfits. So be on the lookout while going for the other band members. Head out of the cave to get to the Fire Kingdom and talk to FP. After you get done talking to her, you'll find the last snail just to the left of her. Flambo will agree to help you with your plan for FP if you bring him some coals. Meanwhile, if you try to take the portrait of FP, you'll get in a fight. Take it again and you'll find one of PB's outfits.
If you go into the kitchen, you'll end up having to pay for the mess you made earlier by cleaning up the soup still on the floor. Pick up the mop and clean it up, getting you a stick and uncovering a coal. Return to the main room and give the fire wolf pup the stick to get a second piece of coal. These two pieces will end up securing you Flambo's note. He'll also allow you to get up to Cinnamon Bun, but CB won't give you a note unless you can inspire him. Thankfully, the portrait of FP will be all that he needs.
Part 3b: LSP on Vocals
LSP won't sing for you since you made a mess of her previous plans. Mentioning her fans will make her sing a different tune, though, and she expects to see them in the clearing soon. Go into the background and collect the bucket and rope from the well using your sword, then leave via the forest path. Use Jake to collect the second of PB's outfits hanging from the tree, then continue on the path until you get to Tree Stump. Request for it to be one of LSP's fans to find one of the conditions. If you head to Tree Trunks' place, you can request to borrow her shovel, a seed, and for her to be one of LSP's fans as well. Using the shovel, return back to the bridge past Tree Stump and collect some dirt. Combine the dirt with the bucket, then put the seedling in it. This is the treat that Tree Stump is wanting. Returning to Marceline's, use the stick with rope to make a fishing pole. Use this to fish out the last of PB's outfits and finish the case!