These Pokemon can learn beat up:
- Houndour, Houndoom
- Sneasal, Weavile
- Charmander, Charmeleon, Charizard
- Ekans, Arbok
- Nidoran♀, Nidorina, Nidqueen
- Nidoran♂, Nidorino, Nidoking
- Diglet, Dugtrio
- Mankey, Primeape
- Aimpom, Ambipom
- Seedot, Nuzleaf, Shiftry
- Cottonee, Whimsicott
- Sandile, Krokorok, Krookodile
I think that the most viable users of this attack would be Weavile, Krookodile, Shiftry and Ambipom.
The first 3 all get STAB and have a higher attack that special attack, and is more powerful than any other of their physical Dark type STABs when there are 6 Pokemon left.
The next option may sound a little strange, but Ambipom is actually a very viable user of Beat Up. It gets coverage on Ghost types, which is important as it will draw in many Ghost types due to its Technician STAB Fake Out, and can easily hit harder than Shadow Claw because of Technician.