Phoenix Point

I believe this is buggy at time of writing, will update once I know more.

Once you've unlocked the Recruitment Protocols research there are I believe seven distinct classes to recruit.

You can only recruit from a faction if you have at least a Friendly diplomatic status.

A Haven indicates it has a soldier available for recruitment if you zoom in on the Geoscape and the Haven icon has a little yellow human figure shown at the lower right. A figure with a Star indicates it's an Elite class of soldier.

Here are the various classes and their faction restrictions

Assault
Basic soldier available from all factions early in the game

Heavy
Basic soldier only available from New Jericho faction early in the game

Sniper
Basic soldier available from New Jericho and Synedrion factions early in the game

Beserker
Basic soldier exclusive to Disciples of Anur faction early in the game.

Technician
Elite soldier exclusive to New Jericho faction

Priest
Elite soldier exclusive to Disciples of Anu faction.

Infiltrator
Elite soldier exclusive to Synedrion faction


By clicking on the Haven info you can see the recruitment information which gives the soldier class icon indicating the class of the soldier you will recruit - very handy. If the recruitment section says "Elite" then their elite class will be available only. This brings me to the rub...

Important - Early in the game the factions allow their basic classes available for recruitment but as the game progresses the havens start researching elite training and these standard classes become harder to find as the Haven researches Elite training.

Also note that although you start with an Assault, Sniper and a Heavy you will need to additionally recruit one of each for this achievement.

Update: After progress sat at 85%m equating to 6/7 for a long time, on a sixth playthrough it unlocked when I went on a Anu recruitment drive, it took a Priest with a Judgement head mutation to unlock. So it may be that for Anu the beserker and priests need head mutations, either that or over your playthroughs each mutation combo is needed. It's still unclear.