When a Pokémon with Beast Boost directly causes another Pokémon (including allies) to faint by using a damaging move, its highest stat (other than HP) is increased by one stage. If this stat is already at +6 stages, Beast Boost will not activate (not even in the case of a tie of two or more stats).
For determining the highest stat, Beast Boost does not take into account stat stages, held items, or reductions due to status conditions; however, it does consider the effects of Power Split, Guard Split, Power Trick, Wonder Room, and Speed Swap. In the case of a tie between multiple stats, it increases one stat, prioritized in this order: Attack, Defense, Special Attack, Special Defense, and Speed.
If the Pokémon fainting ends the battle, Beast Boost will not activate. Beast Boost activates after the Pokémon gains Attack from Fell Stinger. If a Pokémon with Beast Boost defeats a Pokémon with Mummy using a contact move, the Pokémon's Ability will become Mummy before Beast Boost has the opportunity to activate.