One highly-recommended Cat for this stage is Ectoweight Cat. He outranges Lord Gravey and can easily knock him behind the base. Combined with fast-moving cats like Maglev Cat, Lion/Manic Lion Cat, and Awakened Bahamut Cat, you can destroy the enemy base before Miss Haka can reach yours. All you need are some meatshields, a couple of high-damaging Cats to deal with the Skelecats and Sa-bats (such as King Dragon), and a Knockback up combo. Then, the stage can be cleared with Cats even below level 30 and without powerups. Just spam Ectoweight, meat shields, and high-damage cats until Lord Gravey is behind the base, then send in Bahamut.
If you don't happen to have Ectoweight, you can just do it the The Haunted 1LDK way: use ranged attackers like Macho Leg Cat, Dragon/King Dragon Cat, their Crazedcounterparts, or Vaulter Cat, paired with a ranged or slow meatshield. It is recommended you bring a Rich Cat. Start off by using regular meatshields and stacking some ranged attackers. When Miss Haka spawns and gets near your cats, stop sending out your regular meatshields and start sending out your slow meatshields, such as Boogie Cat. His slow speed will help protect your attackers while also preventing Miss Haka from burrowing. If you stacked enough ranged attackers, they should be able to permanently knockback Miss Haka before she gets the chance to burrow. If she happens to burrow, use a fast cat like Maglev Cat to snipe her in case of an emergency. Repeat this until Lord Gravey is dead. Once he's dead, you're going to have to hope that your attackers finish off the base before Miss Haka arrives at your base.