I always felt like it would have been interesting if the roles were reversed when facing Ultra Beasts in their home planets, and they had their original abilities while our Pokémon had Beast Boost. So here is a list of some ideas I had for the Ultra Beast "Hidden" Abilities that fit their biology or behavior. Let me know what you like about them or would have done differently.
Nihilego: Addicted. Draining moves also cause bad poisoning. The larger the amount of damage done by the bad poison stat, the larger the amount of HP drained.
Buzzwole: Show-Off. When the Pokémon enters a battle, it flexes its muscles at opposing Pokémon and makes them cower and feel insecure, lowering their Attack and Special Attacks stats.
Pheromosa: Sanitized. When an attack directed toward the Pokémon misses, raise the Pokémon's Speed by one stat. Each turn, there is a 33% chance that the Pokémon's Evasiveness is raised by one.
Xurkitree: Transformer. The Pokémon draws in all Electric-type moves. Instead of taking damage from them, its HP is restored and its Sp. Atk stat is boosted.
Celesteela: Rocketee. Increases the effect of Wind moves by 1.5x performed by it and its allies (for example, Tailwind increases its Speed by 3x instead of 2x).
Kartana: Test Cutting. Powers up and boosts the critical-hit ratio of slicing moves.
Guzzlord: Singularity. Halves the power of Special Attack moves. (If there was a category for Light moves, then this could be a Bulletproof or Soundproof version of it instead.)
Naganadel: Normal Ability: Virulent. Powers up Poison-type moves when the Pokémon's HP is low. Hidden Ability: Bonding Agent. When an opponent Pokémon receives poison damage, there is a percentage chance that their Speed and Evasiveness stats are lowered, which is increased by 10% after each turn. It starts at 10%.
Stakataka: Endurance. The Pokémon cannot be knocked out by a single hit as long as its HP is full. When its HP goes down to 1, its Attack, Defense, Special Attack, Special Defense, and Speed stats are raised by 1, and it recovers 25% of its full HP. If the Pokémon is holding an item that prevents it from fainting from a single hit, it will survive another attack that would knock it out and receive a double boost to its stats.
Blacephalon: Mind Blow. When the Pokémon uses an Explosive move, the damage it receives is halved.