You can find the Ratslayer in the Broc Flower Caves located at the southeastern region between Nipton and the Bloodborne Cave. To locate the cave without aid of the Explorer Perk, seek out the Atomic Wrangler owner and speak with the sister Gerret. Accept the work of Debt Collector and find a woman and persuade her to cough up the money.
She'll give you half of what she owes and gives you the exact location of the cave.
In the cave, follow the tunnel until you find the cliff edge of the main chambers filled with huge frickin' rats. On the edges of the main chamber, follow it to a room where the Ratslayer is sitting on the desk to your left.
Inside the rest of the room is lots of medical supplies (stimpaks, doctor bags, etc).
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