There are 8 Legion Arms In Lies of P.
1) Left Arm of Steel - Starting Legion arm
2) Puppet String - Talk to Eugenie when you first get to Hotel Krat
3) Fulminis - After killling Scrapped Watchman Boss, turn the Overcharged Storage Battery in to Eugenie or Venigni for Fulminis.
4) Flamberge- After killing King's Flame, Fucco, craft the legion arm at Venignis workshop with the High Powered Flame amplifier.
The next 4 arms can be crafted with Legion Plugs
Legion Plug 1 - Found in a chest in St. Frangelicos Cathedral (when working your way up some wooden platforming)
Legion Plug 2 - Found in a safe in a house in Rose Isabella Street
Legion Plug 3 - Found in a chest in Grand Exhibition
Legion Plug 4 - Reward for killing an elite enemy when you go back to Krat Central Station later in the game
With all 4 legion plugs you can craft the remaining legion arms at Venignis Workshop.