If I have a Ahri Nine Tailed Fox Legend and the enemy attacks a battlefield with Assault, does the effect from Ahri apply before or after the Assault effect?

Yes — Assault applies first, then Ahri's -1 Might.

Assault is a passive ability that takes effect the moment the unit gains the Attacker designation, before any triggers go on the chain. Ahri's Nine-Tailed Fox ability then triggers on that designation and resolves afterward, reducing the already-buffed Might. So a 3-Might unit with Assault 3 attacks at 6 Might, then Ahri brings it to 5. This matches FAQ 213 and Rule 807.1.c (Assault is a passive, not a trigger).