Adamant for Choice Band Tyranitar, Jolly for Choice Scarf or Dragon Dance, Hasty for Lure, Quiet for Boah, Careful for Curse, and Naive for Mixed are the best natures for Tyranitar. I guess you could use Brave with a
Boah moveset, but it won't deal much damage to physical walls which is why you should even use Boah.
Bold is a poor nature for Beldum, you don't want to decrease Attack so use Impish (+ Def / - SpA). Though, that's if you want a really defensive moveset which Bronzong does better in my opinion. Adamant is the best nature for Metagross, and Jolly is okay too for Agility and Choice Scarf.
Brave is acceptable for Machop, but Adamant is slightly better because Machamp can then outrun a few Pokemon like Blissey.
Lonely is terrible for Empoleon, you shouldn't use any physical movesets for it (even if you did, use Adamant). Modest is the best nature for Empoleon, and you can use Bold/Calm for defensive variants I guess.
Dragonite's nature is okay for a lead moveset. Otherwise, Rash/Mild for mixed, Adamant/Jolly for Dragon Dance or Choice Band, and Careful for defensive.