This achievement is for defeating Father Wales in Siren Alley.
Father Wales is a Spider Slicer, so be prepared for lots of jumping and climbing from him.
He starts out with a few Leadhead Splicers, kill these guys, and a few more will spawn, as well as a Brute. After killing them, Father Wales will join the fight with a Security Bot and a few more Leadheads.
Simply take out the Leadheads, as well as his bot to make the rest easier. Electrobolt, Hypnotize, and Incinerate make this fight pretty easy. Using Hypnotize on the other Splicers will cause them to attack each other, even Wales, so use that to your advantage.
If you have anti-personal rounds, these are also helpful. I used A-P Machine Gun ammo, and a few Spears.
For those interested, my tonics and plasmids are below.