Button - First you have to turn on the power and pack-a-punch. Go up to the Observation Tower and go to the one of the glass walls and next to one of them will be a small button to press which will start a cutscene.
Part 1 - You will have to kill a tormentor with fire. A tormentor is a fast red zombie that will blow up when near you. The easiest way to kill it by fire is to kill it with a flame thrower. Once do this there will be a part to pick up.
Part 2 - Find a small purple cystal that you can knife you loot but do not knife it. Get and Abomination next to the crystla and wait until it does it lightning attack. Stand next to the crystal so that the abomination hits the crystal. This will spawn a part at the crystal
Part 3 - This will only spawn in once the game says "we've identified something flying in". Go to the Donut Shop at Main Street. Behind the counter should be glowing ball. You have to stand on the ball and kill as many things as possible until it spawns a part underneath it.
Craft - Go to the Particle Accelerator and on one of the walls there will be a big bathtub that you can place the parts into. You now have to get melee only souls at that bathtub. Once you get enough you should be able to get the chrysalax.