Normally how I've done this fight in the Past is PUP(sub WAR), BRD, COR, SCH(RDM or WHM also works), DDx2
Robot tanks one of the goblins PUP main tanks the other but just within healing range of the healer(20-21 yalms) in full PDT set(3 x Nyame/2x Mpaca mix is fine) BRD sleeps BLM and everyone zergs the Don, after everyone assists the pup, then kills robots target then finally kill the incanter.
Regen V/Phalanx on the PUP in a phalanx set makes tanking the other goblin pretty trivial sometimes might not even need the occasional heal at all. Depends how fast you kill the don.
I like it when there’s a good reason to use my PUP, so this is basically the setup we have been running. PUP SCH BRD DDx2-3 CORx0-1 (COR prob ideal but there’s a lot of flexibility). Can be helpful to bring a frontline healer (e.g., BLU DNC whatever) and/or have the BRD come /WHM and play backup healer for times when the main healer eats it and is getting back up.
A few additional PUP notes:
Automaton on the DRK and PUP on the WAR is best, because the DRK can cast Break and that’s far more annoying on the PUP.
SCH Regen V was plenty for me to be in no danger on PUP while TPing in full Malignance (plus Moonbow +1, Odnowa +1, and JSE cape PDT-10 to hit DT-40%/PDT-50%, which was honestly overkill - tbh I should at least ditch the unnecessary earring).
Turtle build automaton was also in absolutely no danger with auto repair kit regen only and normal tanky attachments. No need for any pet DT gear on the master. Also no need for Repair for survival, did use it once to deal with a fluky DRK Break that was cast right as I was setting up, so something to keep in mind but that was only for the status effect removal. You might also want to use it if the puppet is stoned when the whole group is moving to go kill its goblin.