Thus far, the only DLC needed are the four campaign DLCs (Captain Scarlett and her Pirate's Booty, Mr. Torgue’s Campaign of Carnage, Sir Hammerlock’s Big Game Hunt, and Tiny Tina's Assault on Dragon Keep, all included in the Season Pass). The Mechromancer Pack, Psycho pack, Ultimate Vault Hunter's Upgrade Pack, Collector's Edition Pack, Creature Slaughterdome, and various outfit packs have no achievements.
If Gearbox continue to release DLC, this is almost certainly the pattern they will follow; DLC which adds a significant amount of new quests will include achievements, DLC which does not (new characters, skins, items or smaller content like the slaughter dome) will not.