Strategy I used: Dipper Yuly x 1, Evasion axes +1 x 2, decent reward set, call beast/reward merits, full set of healing temp items, *Powder boots/movement speed+,RR/Ducal, and /NIN.
*Powder boots not needed, but help when you are just getting started.
You "spawn" Fistule by dragging an NM to it. Guimauve (lottery pop), or Bloodguzzler (forced pop) both work fine. When you drag the nm to him it will use dissolve which is a conal AoE, but can be easily dodged by you and your pet with some easy maneuvering. The damage should be ~800 to Yuly, so either heal, or let it take a couple hits before you worry about it. Drag Fistule far north, preferably over the hills. You can melee with Yuly standing opposite of it, throwing in some nice damage to speed up the fight. Use Spiral Spin when tp is up, but if you feel Yuly is dodging fairly well feel free to use Noisome powder (goal is to evasion tank though).
Around 84% hp Fistule will use Cytokinesis, spawning 2 Pustules. Now is a good time to use Reward if Yuly is dipping around 50~60%. Disengage from Fistule, and get to max casting range and pull both Pustules. With both Pustules on you start running south, thanks to the horrible pathing thanks to the terrain you should be able to get a good lead on them. Try and stay ~25 yalms away. After taking them so far away from Fistule they will despawn. Run back to Fistule, and if Yuly's health is running low toss it a Reward. Rinse and repeat until dead.
Points of interest:
Some of you may be wondering why I used /nin over /whm or /sch.
Dissolve: Conal true AoE 800 or less damage.
Mucus Spread: AoE slow, unsure on radius.
Epoxy Spread: AoE bind, 2 shadows absorb it.
Cytokinesis: AoE ~20 Gravity, spawns 2 Pustules. 2 shadows absorb it. Uses approximately every 20%
Pustules if you kill/use Fluid Spread will split into 2 more pustules. At max there can be 8 Pustules at one time.
If you do not despawn the Pustules when dragging them away they will go to the main area, and slowly work their way back to Fistule.
Alternative strategy is to Kite the Pustules, as Fistule can only have 2 spawned from Cytokinesis at a time.