There are 6 Augmented Weapons you must get kills with:
- Blaster
- Railgun
- Amped Bolts
- Death Ray
- Boom Eternal
- Lightning Tornado
From what I can find and tell from my own experience, the kills will carry over even after death. This achievement is much easier on story, but can obviously be done on any difficulty. You don't need to get all of the upgrades for each weapon, you can just buy the third slot for them. This takes a ton of money, so you probably won't get this until your New Game+ playthrough that carries over all of your earnings. Death Ray and Lightning Tornado will probably take you the longest due to cooldowns, so make sure to do them on weak enemies! Below is not my video, however am simply adding it for those who prefer a video as opposed to text: