This NP1 Valkyrie comp with any level MLB IE is not really a budget comp, but can work if you don't have a Kaleidoscope or your own Waver (or Skadi, or Helena).
It's able to farm 40AP doors (guaranteed) because of the Caster enemy boost to NP generation and because Valkyrie gets a lot of overkill hits from the silver doors. Because of these requirements, this comp won't work as is against high level event quests, which typically have higher hp enemies and minibosses.
(HP numbers are per enemy, assumes man attribute)
Against Casters:
Turn 1 requires 6 total overkill hits (19565 hp)
Turn 2 requires 0 overkill hits (27174 hp)
Against Archers:
Turn 1 requires 15 total overkill hits (10729 hp)
Turn 2 requires 4 total overkill hits (2 enemies 53648 hp, 1 enemy 38626 hp)