Proven Strength

You also need to be revered with Golden Lotus to even begin doing these dailies and revered with Shado-pan to finish this achievement

Companions are split into three parts restricted by rep and then a further three groups restricted by today's opponent.
Tier 1: You start with these.
Tier 2: Unlocked at honored.
Tier 3: Unlocked at revered.

Mogu:
Fei Li (tier 1)
Snow Blossom (tier 2)
Yalia Sagewhisper (tier 3)

Yaungol:
Protector Yi (tier 1)
Chao the Voice (tier 2)
Lao-Chin the Iron Belly (tier 3)

Mantid:
Taoshi (tier 1)
Hawkmaster Nurong (tier 2)
Tenwu of the Red Smoke (tier 3)

Each companion requires having done a fight with them and winning but you can only do such fights when you can use their aid with the threats in the groups listed above.

Put simply, I can't fight Hawkmaster Nurong for his help because today the dailies have me kill Mogu. I can, however, fight to unlock Snow Blossom instead.

Just a little heads up on anyone joining MoP late into the game , like me: You usually had to be be Revered with the Golden Lotus to even begin doing the Shado-Pan dailies (as already mentioned in an above post). However, I joined late on and this changed, meaning you could go right into the Shado-Pan dailies without the need to grind rep for Golden Lotus.

My problem here was, because I completely bypassed the Golden Lotus rep grind first, I wasn't sure why I wasn't getting credit for a few of the company - Fei Li and Protector Yi were a couple that wouldn't appear up, even though I'd gotten credit for them both for the achievement Getting Around with the Shado-Pan.

Anyhow, after deciding to grind rep for Golden Lotus, when I hit revered with them I immediately got the achievement for Proven Strength, much to my surprise.

So, to put it shortly, if you don't seem to be getting credit for a few of the company and you're not revered with the Golden Lotus, then go and grind!

I had every achievement with shado-pan completed except this one. I couldn't train with Fei Li, Protector Yi, or
Taoshi. As soon as I got Revered with Golden Lotus, this achievement unlocked and completed instantly.