The report is given to you by LeChuck in the second half of Part II. It has 5 items to fill, but the achievement requires 8 unique entries. This means you can just save, fill five different ones, then load the game and fill it again using different occurrences of a mess.
Here is the list:
- Ghost rats outside LeChuck's cabin
- Galley (kitchen) - use report on any item there, it's all messy and counts as one entry
- Grease on the barrel of chicken feed in the hold (or it can be on Guybrush's kitbag, depending on where you transferred it during swabbing)
- Grease on the porthole
- Poop of one of the ghost chicken in the hold (first feed the middle chicken - Molly - then leave the room and come back)
- Empty crates all over the deck
- Leftovers of the potion spilled near the cauldron on the deck
- Gullet being stuck in the ship's rudder (underwater)