Bleed Me Dry involves gathering creature eggs for the arena known as the Thorn.
The tasks are given one at a time. The final tasks are Cazadors and Deathclaws, so it helps to have strong companions, high crit. chance strong wep, and lots of HP.
For max caps, have 90 barter or 70 barter+some salesman weeklies.
The first task is Giant Mantises. There nest is within Vault 22. Consult this video: http://youtu.be/gYq7haywNBw
The Mantis nest is within the caves linking the 3rd and fifth levels of the Vault. Entering the fifth level through the elevator, go up the stairs on your left and enter the door to the caves. If you don't the repair skill necessary to fix the elevator, find the keycard in first 4th level (find the hall with the first bedrooms, look on the metal shelves in the first one to your left) and backtrack to the 3rd level cave entrance.
The next task is Radscorpion eggs. Easy task if you don't allow yourself to get surrounded. Go to Goodsprings and follow your quest marker.
Third is fire geckos. Their nest is an unmarked cave. It's near Novac and Ranger Station Echo. Approach the cave watching out for Fire Geckos. You can use a stealth boy to speed through to the eggs and immediately flee. There are no unique items in the cavern.
Fourth, Nightstalker eggs. Easiest task ever if you have the Animal Friend perk. The Bloodborne Cave they inhabit is circuitous; there's only one way to go. Descend into it until you find the eggs. Near the eggs, look for a key next to the campfire and backtrack to a fenced off section of the cave. Open the gate, disarm the tripwire, and check the trunk for lots of caps before leaving.
Fifth, Cazador eggs. Their nest is in the open air. You could approach via Red Rock Canyon, but glitching through the mountain pass to them is tricky. A better bet is to make the hike from Ranger Station Foxtrot or Jacobstown. When you find the nest, loot the near by Super Mutant Master and report to Lucy.
Last, Deathclaws. Two options: Quarry Junction or Dead Wind Caverns. Quarry Junction is easy if you swept through it before. Otherwise, the Dead Wind deathclaws are actually weaker stats-wise than the Quarry ones with the exception of the Legendary Deathclaw, but he can be avoided and safespotted if he gets stuck in a tunnel.
The Legendary Deathclaw guards the unique grenade machine gun Mercy. Try to get it before you leave.
Return to Lucy for your final payment and sex.