Your Dachsbun will likely never consume its Babiri berry, and also never get hit with Iron Head
Depends. If Iron Head remains Incineroar's strongest move even with Babiri factored in, it might still go for Iron Head. Of course, a neutral EQ or Acro will be stronger than neutral Iron Head so that is unlikely to be an issue if either is included in Incineroar's kit.
You might need to run Coba Berry or Weakness Policy to ward off Acro, so Incineroar doesn’t fish for an Acro crit that hits you for 75%. (AI also cheats to vaguely avoid activating weakness policy.)
Since Shell Bell is required for ID+BP strats, Coba Berry won't really be an option for these sets.
Seeing how Incineroar is vulnerable to being burned, the usual Inferno Torkoal

strategy is likely to see success. Especially since Bulk Up or Swords Dance are also likely to be included, necessitating Clear Smog support.
Of course, a funnier alternative to Torkoal is:
Magcargo @ Leftovers / Light Clay
Ability: Flame Body
Tera Type: Fairy / Fighting / Dark (whichever resists Dark and isn't weak to coverage)
EVs: 252 HP / 252 Def / 4 SpA
Bold Nature
- Reflect
- Recover
- Mud-Slap
- Clear Smog
Obviously this set won't work if EQ or Brick Break are in play. However, with Reflect and Recover being in play, Incineroar is very likely to get burned by Flame Body at some point with it many contact moves being used. After that, Incineroar's damage output should be reduced to so little that you can afford to Mud-Slap and Clear Smog to keep Incineroar from being able to put out any meaningful damage.
Gouging Fire @ Leftovers
Ability: Protosynthesis
Tera Type: Fairy
EVs: 252 HP / 4 Atk / 252 Def
Impish Nature
- Burning Bulwark
- Breaking Swipe
- Morning Sun
- Dragon Cheer
Alternatively, you could rely on Burning Bulwark for burning needs. With Breaking Swipe for further damage reduction, Clear Smog wouldn't be needed as much. The last slot is a generic support slot that could go to Dragon Cheer, Howl or Will-o-Wisp.
As a side note, side targeting your own team's Dachsbun with Wisp and other Fire moves is going to be fun.
Ho-Oh @ Leftovers
Ability: Regenerator
Tera Type: Fairy
EVs: 252 HP / 4 Atk / 252 Def
Impish Nature
- Sacred Fire
- Reflect
- Life Dew
- Will-O-Wisp / Helping Hand
More burning tricks, this time with Ho-oh. Your options for support are somewhat limited outside of Reflect and Sacred Fire but being a Life Dew bot is pretty useful even if that's the only thing you can do between refreshing Reflect.