There is only one type of chubby in this standalone game: a Skeleton named Chubby Bones.
These are very, very rare and this is RNG based. So you are going to be either very lucky, and find him in a normal playthrough, or like me, you will have to simply grind it out.
I had done everything there is to do in the game, and so to succeed with this I chose the following path:
Take your highest level character, in my case a Gunzerker, level 35 and fast travel to Flamerock Refuge.
Then head to the exit to go back to Unassuming Docks and do a save and exit.
This will pin your starting point.
Each time you start the game, you will commence at this spot. Now turn right and run down to where 4 normal skeletons (and some others) usually spawn. You are heading in the direction of Mister Boney Pants Guy (who incidentally will spawn each time).
If none of the first 4 skeletons you encounter are Chubby Bones, then immediately save and quit, then restart again.
Rinse and repeat until he finally spawns.
It took me around 150 attempts before he finally appeared. As I say, he has an extremely low spawn rate.
I did this on TVH mode, but he can appear in Normal mode as well. I had the ‘easy’ gameplay option switched off, not sure if this makes a difference.
He can be quite tough to take down, so if you meet him very early on in your playthrough, be prepared for a tough fight. In my case, with a level 35 maxed out Gunzerker carrying a Conference Call weapon, he went down in 3 shots.
The places he can spawn (to look out for) are in the Unassuming Docks, Immortal Woods, Lair of Infinite Agony and Flamerock Refuge. Basically the places where you encounter skeletons.
I chose this single spot in Unassuming Docks for the quickest rinse and repeat.
Be careful if you need this trophy when playing in co-op, only the player delivering the final blow will get the trophy.
Good luck!