The achievement unlocks after defeating the chapter's boss, after a wrap-up cut scene, when the mission results appear.
There is some minor fighting in the level, and new moves introduced. Also, the "gun" arm is unlocked and explained. The level amounts to going through short areas of the house to retrieve "things" (three of them in all) to give to Alisa.
In the room with the strange lamp that Mika comments on, you have to use the gun arm (where it's introduced) and shoot all four lamps in a short amount of time to continue.
The boss battle was a pain, playing on Hard as the first time through. I assume it's less challenging on Easy or Normal (and especially on subsequent replays, when you've applied quite a few upgrades).
Here is my strategy for beating the boss.
There are three stages to the battle. The first two are nearly identical, although it may move a little faster in the second one (uncertain). For both stages, get up close when it's standing on the ground, and get in hits with X. Use B or move+B for dodging and countering, and keep hitting until it climbs the wall.
While it's on the wall, shoot it. Try to be accurate so that "blood" waste is minimized. Several hits will cause it to fall off onto the floor on its back. Get in as many more hits as possible until it climbs the wall again.
To finish each stage, you have to (A) deplete its health bar, and (B) have it down on the floor on its back. If it's on the wall or standing, it doesn't matter if its health is gone. You can't put in a final blow.
When it climbs the walls you're safe, except when it goes up to the ceiling. Then, it will shoot some kind of purple goop, which you'll need to just run from or dodge with B.
Once it's on its back and no health, you'll get a prompt to hold RT. Get in close for that, hold RT, and hit X to slice off a limb. It'll recover, so repeat pretty much the same tactic for the second stage.
In the third stage, it will begin to throw "egg" things, not just purple goop, which hatch and become big face bugs. I found that I would get hit by them when trying to attack, and shooting them wastes "Blood" making it more difficult to finish off the boss when the time comes, so a better tactic was just to keep on the move. It seems that in this stage, it won't fight you on its feet. You either have to shoot it off the wall, or hit it when it falls off onto its back. So keep moving to avoid the little critters, and keep shooting it with as good of an aim as possible when it's on the wall or ceiling, to get it to drop.
Once it's down and has depleted health, do what you did before. Get in close, hold RT, and X.
Now, this takes "blood" which appears as those little rose symbols on the health bar. If you run out of "blood" you can't do the power move to finish it off. This is true in all three stages. Attacking it directly fills the "blood" meter, but shooting with the "gun" arm depletes it. In the third stage, in addition to moving to avoid the critters, I found it best to hold down the trigger to rapid-fire when it was still -- either on the wall, or especially on the ceiling shooting its critter-eggs.
Once I got it right, I still used one or two Mika cards to revive and get through the battle. But results may vary.