So for these achievements you need to talk to each of them in all their locations, expend their dialogue AND summon them for 3 boss fights WHICH THEY MUST SURVIVE, after which you can talk to them in their final locations and they will give you their gear. Now this sounds like a massive ball ache and it can be, but only if you are playing offline or and/or don't know the tricks.
So firstly talking to them, I won't go into this as you can find out all their locations yourself, only one location is a bit tricky and it is Lucatiel whilst she is in Black Gulch because the location is INCREDIBLY hard to find on your own.
The tricky part of these achievements is keeping the summons alive during boss fights, which are:
Lucatiel (need to summon and have her survive 3/4):
Flexile Sentry
The Rotten
Lost Sinner
Smelter Demon
Easiest are the first 3, Smelter just has too much AoE capable of one shotting her.
Benhart:
Prowling Magus and Congregation
Looking Glass Knight
Giant Lord
Only three that matter, all incredibly easy as Benhart is tough as nails.
To make these fights the easiest thing in the world, you need 3 things.
1. Redeye Ring - Purchased from Shalquoir, makes enemies focus you and only you.
2. Greatshield - 100% phys resistant, 2 hand it.
3. NPC phantom + player phantom.
Equip the ring, 2 hand your shield and watch your buddy and the NPC kill the boss with zero stress, you will take zero damage and never lose your stamina, ever, even if you keep up block at all times.
This tactic makes keeping Lucatiel alive a joke, Benhart is a different matter as he's genuinely useful, Prowling Magus is the new Pinwheel but easier, Looking Glass Knight is not overly hard and you only really need the Redeye Ring, Giant Lord is incredibly easy as the only real threat to Benhart is a boulder.
Once you've done this, all you need to do is talk to the NPC in their final places, for Lucatiel this is Shrine of Amana and Benhart you can talk to in the Memory of Oro, if you talk to them before completing the boss requirements and talking to them in their other places, you will NOT get their gear.
Oh and if you've already killed the bosses without them, you can do it in NG+ or by using Ascetics.