Body Press is learned by 3 species by level and 154 by machine

Effect, in PokéAPI's words

“Damage is calculated using the user's Defense stat as its Attack, including stat stage changes.”

Who learns it

154 species in all, 3 games

Scarlet and Violet: 119 species

Species	Method	Level
Regigigas	Level up, Machine	42
Raging Bolt	Level up, Machine	84
Blastoise	Machine
Jigglypuff	Machine
Wigglytuff	Machine
Graveler	Machine
Golem	Machine
Slowbro	Machine
Hypno	Machine
Rhyhorn	Machine
Rhydon	Machine
Lapras	Machine
Snorlax	Machine
Dragonite	Machine
Mew	Machine
Meganium	Machine
Sudowoodo	Machine
Quagsire	Machine
Forretress	Machine
Skarmory	Machine
Donphan	Machine
Tyranitar	Machine
Swampert	Machine
Slaking	Machine
Makuhita	Machine
Hariyama	Machine
Nosepass	Machine
Swalot	Machine
Numel	Machine
Camerupt	Machine
Torkoal	Machine
Grumpig	Machine
Tropius	Machine
Metagross	Machine
Regirock	Machine
Regice	Machine
Registeel	Machine
Groudon	Machine
Torterra	Machine
Rampardos	Machine
Bastiodon	Machine
Bronzong	Machine
Hippopotas	Machine
Hippowdon	Machine
Abomasnow	Machine
Magnezone	Machine
Rhyperior	Machine
Mamoswine	Machine
Probopass	Machine
Dialga	Machine
Palkia	Machine
Heatran	Machine
Arceus	Machine
Emboar	Machine
Eelektross	Machine
Cubchoo	Machine
Beartic	Machine
Golurk	Machine
Cobalion	Machine
Reshiram	Machine
Zekrom	Machine
Kyurem	Machine
Chesnaught	Machine
Hawlucha	Machine
Carbink	Machine
Goodra	Machine
Avalugg	Machine
Diancie	Machine
Volcanion	Machine
Crabominable	Machine
Mudsdale	Machine
Kommo-o	Machine
Rillaboom	Machine
Greedent	Machine
Corviknight	Machine
Drednaw	Machine
Carkol	Machine
Coalossal	Machine
Appletun	Machine
Sandaconda	Machine
Grimmsnarl	Machine
Falinks	Machine
Stonjourner	Machine
Cufant	Machine
Copperajah	Machine
Duraludon	Machine
Zamazenta	Machine
Urshifu	Machine
Glastrier	Machine
Calyrex	Machine
Ursaluna	Machine
Oinkologne	Machine
Pawmot	Machine
Dachsbun	Machine
Naclstack	Machine
Garganacl	Machine
Orthworm	Machine
Houndstone	Machine
Cetoddle	Machine
Cetitan	Machine
Dondozo	Machine
Clodsire	Machine
Dudunsparce	Machine
Great Tusk	Machine
Brute Bonnet	Machine
Slither Wing	Machine
Sandy Shocks	Machine
Iron Treads	Machine
Iron Hands	Machine
Iron Thorns	Machine
Baxcalibur	Machine
Wo-Chien	Machine
Ting-Lu	Machine
Roaring Moon	Machine
Koraidon	Machine
Okidogi	Machine
Archaludon	Machine
Hydrapple	Machine
Terapagos	Machine

Brilliant Diamond and Shining Pearl: 2 species

Species	Method	Level
Regigigas	Level up	42
Probopass	Level up	50

Sword and Shield: 87 species

Species	Method	Level
Regigigas	Level up, Machine	42
Blastoise	Machine
Nidoqueen	Machine
Nidoking	Machine
Slowbro	Machine
Onix	Machine
Lickitung	Machine
Rhydon	Machine
Lapras	Machine
Snorlax	Machine
Dragonite	Machine
Mew	Machine
Sudowoodo	Machine
Steelix	Machine
Mantine	Machine
Skarmory	Machine
Miltank	Machine
Tyranitar	Machine
Swampert	Machine
Aron	Machine
Lairon	Machine
Aggron	Machine
Wailmer	Machine
Wailord	Machine
Torkoal	Machine
Claydol	Machine
Walrein	Machine
Relicanth	Machine
Metagross	Machine
Regirock	Machine
Registeel	Machine
Bronzong	Machine
Hippowdon	Machine
Magnezone	Machine
Lickilicky	Machine
Rhyperior	Machine
Mamoswine	Machine
Dialga	Machine
Palkia	Machine
Heatran	Machine
Roggenrola	Machine
Boldore	Machine
Gigalith	Machine
Darmanitan	Machine
Crustle	Machine
Cofagrigus	Machine
Garbodor	Machine
Ferrothorn	Machine
Beartic	Machine
Golurk	Machine
Reshiram	Machine
Zekrom	Machine
Kyurem	Machine
Hawlucha	Machine
Carbink	Machine
Goodra	Machine
Avalugg	Machine
Diancie	Machine
Volcanion	Machine
Mudsdale	Machine
Bewear	Machine
Turtonator	Machine
Dhelmise	Machine
Kommo-o	Machine
Guzzlord	Machine
Stakataka	Machine
Melmetal	Machine
Rillaboom	Machine
Greedent	Machine
Corviknight	Machine
Dottler	Machine
Orbeetle	Machine
Dubwool	Machine
Drednaw	Machine
Carkol	Machine
Coalossal	Machine
Appletun	Machine
Sandaconda	Machine
Grimmsnarl	Machine
Obstagoon	Machine
Runerigus	Machine
Stonjourner	Machine
Cufant	Machine
Copperajah	Machine
Duraludon	Machine
Urshifu	Machine
Glastrier	Machine