How do you collect all the crew types?

I got this achievement yesterday, and the difficulty is that it is relatively random. However, I'll share my anecdotal advice.

First, hit all the shops you can. Shops don't always have crew, but there's a chance that they might. I've found that shops in a sector belonging to a particular race tend to have that race more often, but it's random - sometimes I've been in Engi space and seen a shop full of Zoltans, for instance. Crewmembers tend to cost less than 100 scrap, but I'd suggest trying to have ~100-150 scrap on hand just in case you find a shop that's got 2 races you need.

One event that I believe is more common in "pirate" and "civilian" sectors is an encounter with a slaver. They may attempt to extort you to give them either some scrap or one of your crew members. If you fight instead, they may later attempt to surrender by offering you a crew member.

From time to time when fighting a ship and killing its crew, I've been told it was a prisoner transport ship and that one of the prisoners wanted to join me. I'd suggest attempting to take ships intact for this reason. I haven't seen any indications in the initial system event that would indicate whether a ship is likely to give a crewmember if taken intact, though.

There are also events where you find a lone survivor on a deserted station, and this can sometimes provide you with an additional crewmember. However, there's also a chance that they will go crazy and murder one of your existing crew, so this is not always a reliable way to make progress towards this achievement. Commenters have noted that having a level 2 medbay can counter this, as can a slug crewmember.

To be honest, I found the other two a lot easier to get (All Installs is challenging on Normal, but trivial on Easy, and Tough Little Ship was actually quite fun to get), and then discovered that

The alt form comes with 3 different species, which means you only need to find an Engi, a Rock (easy) and a Slug(slightly more challenging), and you can get the achievement with that ship

It's a bit of a cheat, but considering that the other two are relatively easy to get, I'd recommend going for them instead.

If you are dead set on getting this one using the Kestrel, then you need to focus on capturing over killing, so basically Transporters, Boarding Drones, Bomb and Fire Weapons, and Sensors. Spot 'em, blast and burn them, and then beam over for the coup.

You also want to focus on aiming for the right sectors.

• If you're missing Slugs, aim for the Nebulas
• If you're missing Rocks/Mantises, aim for the Red Zones
• If you're missing Engi & Zoltan, aim for the Green Zones