Hammerlock wants you to force some Varkids into evolving, then injecting them with something while they are in their pods. Take the injector from Hammerlock and set out for any area with Varkids, like Tundra Express. Once you get to a spot with the Larval Varkids, you want to wait until they go into their pods, which means they are evolving into Adult Varkids.

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Wait until the Varkids go into their pods (left), then run up and inject them to spawn the Mutated ones (right).

If you go up to the pod, you should see a prompt to inject them. Do this and instead of being an Adult Varkid, they will come out as a Mutated Badass Varkid. These enemies are quite challenging and can quickly down you (they are equivalent to Super Badass Varkids and can give quite a lot of XP). After killing the first one, loot the item it drops and Hammerlock says he wants four more. Do the same thing as before, then return to Hammerlock to turn in the mission.