This is a strategy for the boss battle at the end of the level. As the game's levels go, this one is fairly lengthy. But you shouldn't have too much trouble making it to the boss. Basically, stab and dodge, shoot at enemies that are beyond your reach, take out floating enemies first before going for walking enemies (they're easier to kill and can help you avoid taking lots of hits), and press every green panel you come across. In the long hallway before the elevator section, you have to shoot the supports above the catwalk on the left to get it to drop, so you can cross the gap in the floor and proceed. In the trip up to the elevator, you have to keep returning to the middle section to hit the green panel there.
My first time through, the boss was pretty difficult on Hard mode. I only had 3 Mika tickets, and would generally use one almost right away since the checkpoint had me with low health. It took several tries, but this strategy worked for me. On a second play-through on Very Hard, this was MUCH easier. My sword and gun were upgraded to the max (via unlocking the upgrades with yellow moon crystals), and I came fully stocked with Mika tickets from the Store (available from the Office menu, between missions).
There are three rounds to the boss battle.
In round one, he will menace you and swing his arms a lot. Shoot or slice away, but when he ramps up for his swinging arm move, dodge *backwards* a couple times (not to the side) to avoid it. You can block his downward-arm swings much of the time, but in the heat of battle I found it difficult to recognize which attack he was going to do in time.
Once his health is gone, there will come a point where he lashes out his arm, and it stays super-extended for a few seconds. You'll get the RT prompt, so make sure you've got at least one blood rose on your status bar, hold RT, and press X. His arm will come off and get lodged in the wall.
In round two, he adds a couple of things to his arsenal of attacks. One, he will swing up to the ceiling and come toward you for a downward attack. A few times, I managed to dodge-burst (B, then X's when prompted) and get in some good attacks. I also kept my distance and used Musselback to shoot him some (being sure to leave at least one blood rose available to use later).
At times, he will move away and go for his arm that's stuck in the wall. If he retrieves it, you have to pretty much start over to slice it off again, as per the first round. So when he goes for the arm, take what very few seconds you have to aim and start shooting. A few hits will knock him back, and he'll continue with his other attacks once again.
When his health is gone and he extends the arm again, use RT + X to sever the other arm when prompted. As usual, you need one level of Blood to do this.
The third round is timed at two minutes. He's armless now, but still has a powerful area attack. I found no reliable way to avoid it, even moving as far away as possible. Dodge didn't work very well either. I didn't try any other sub-weapon though, so maybe there's a trick to interrupting the attack instead. If somebody knows a great strategy to reliably avoid or stop his third-round attacks, please let me know.
At any rate, you can still get in a lot of katana hits and gunshots against him. Revive with Mika tickets if you need to. Once his health is gone, you get one last prompted attack to finish him off. After the cutscene, the achievement unlocks at the mission stats screen, as with all missions in the game.