Each mission is -- no surprise -- easier on easier difficulties. So if you're just wanting to unlock the achievement for beating the episode without going for other achievements, play them on Easy.
Here are tips when playing on Hard or Very Hard, for beating the level.
Come prepared with a fully-stocked inventory of Mika tickets. Also, it helps to have "Healing" unlocked in the upgrades menu, so you can use LB to channel blood into health. If it's upgraded all the way, this can be done pretty quickly, even during battles.
The mission starts out easy enough, but a short ways in, a 10-minute timer will start counting down. This is after a fairly long radio talk with Vivenne, where you exit the elevator and she tells you Giant Head is going crazy. You have to make your way through a series of rooms connected with locked doors, sometimes opening a new path and backtracking. Additional rooms have bonuses (including a Scarlett location), but exploring too much will leave you without enough time to make it through.
Build up blood with standard melee attacks, and then unleash Adrenaline Rush (RT + X) for one-hit kills on lesser enemies and stunned enemies. This can help level the playing field and help avoid wasted time.
When you reach the stairs, you're almost through. Take out several floating eyes to get the door at the top unlocked. The timed section culminates in a battle in a larger open area, and Vivienne will tell you to concentrate on the large guy first. From what I saw, you still have to defeat all the enemies to get the large door at the end to open, but the enemies (snipers and medium-sized rolling dudes) will keep coming until you do defeat the big guy. Adrenaline Rush helps here too, although you may use blood shooting at the guys up on ledges (try for headshots to make quick work of them). You can also get in one-hit kills against those guys if you're dodging enough and taking advantage of dodge burst (same as for closer enemies, but you basically do a one-hit kill shot after you dodge and get prompted for X). Note that this ability might require a skill upgrade to unlock (needs verified).
The timer (thankfully) goes away after you defeat the big guy. Just finish off any remaining enemies so that the door will open.
In the next section, you'll make your way up into a room where Giant Head will be sweeping the room with laser eyes (from your right to left, if facing forward). Use the large columns for cover, and move as soon as he sweeps left of you. There are floaty gun things, so be prepared to shoot them while in cover to avoid taking extra damage. If you're okay on Mika tickets and health, you can probably just avoid them (you'll probably get hit in the process, but you can keep going).
At the front of this room on the left, you can head outside, and head up to the left to the next room.
There's a big brute in here, and he's a tough sucker to dodge. There are boxes on the right containing health and blood crystals. You can shoot at him, but I would recommend saving the blood gauge for the "Healing" skill (if you have it and need to use it -- take a safe distance then use LB) and for the finishing blow. You're in trouble if you're out of blood, because it's very tough to refill it while fighting him. Luckily, the checkpoint is just before the laser-eye room, so one option is to reload the checkpoint.
If you don't get right up against him -- keep a little distance, but enough that he'll try to attack with his club -- you may be able to dodge and get a dodge burst so that repeated X's do extra damage. I couldn't do this consistently, so I ended up using the gun a little also. After a little while of taking damage, he'll hunch over and you'll get the familiar RT prompt. With at least one blood rose on the meter, use RT + X to finish him.
Leave, go up the stairs, and a panel can be activated to begin the boss battle.
Giant Head has three phases. In the first phase, lesser enemies will stalk you while Giant Head does his thing. Avoid them as best you can. He'll end up killing them for you when he throws large objects, so it's usually not really necessary to focus on them. Just stay away if you can.
When he swings his arm down, block to "catch" it and avoid damage.
For most of the battle, you want to be shooting at the blue ovals on his cheeks (the game calls them his eyes, but they're clearly not), the big one on his chest, and the small one on his neck. Alternate between them so you keep doing damage. This will eventually drain his health bar.
He'll sometimes turn around with his back to you. Here, you have three choices. You can take a moment to use "Healing" (LB) if you have blood to spare. Or you can fight the lesser enemies. Or, you can shoot the small ovals on his back. This won't damage him, but after many hits, it'll yield blood and health crystals (maybe yellow moon crystals too -- needs verified).
When he throws small objects, just move out of the way. When he starts to throw a big object, try to move all the way to the left or the right, so that you have room to move the opposite direction as the large object is slowly approaching you and avoid the impact, which takes a LOT of health if it smashes you.
Once you deplete his health bar, he falls forward. Make sure his head doesn't land on you. Then use RT + X as prompted. If you don't have blood, get up close and melee with X a bit, and as soon as a rose appears full in the meter, do RT + X.
In his second phase, he does the same kinds of things, but he will also add two laser attacks. One is a sweeping attack from your right to the left, which is easily avoid just by moving all the way forward on the platform. The second, he looks down, then slowly raises his head to bring the pair of beams up at you. These can be avoided by moving out of range to either side (preferably the side farthest from the beams).
Continue shooting the ovals on his front and repeat the RT + X to finish his second phase, when his health is gone and you're prompted.
In the third phase, he'll begin trying to smash you with his palm. Get out of the way when this happens, and slice it with X if you're close enough. When he does this, he'll begin tracking you with the eye-beam lasers, so you kind of need to keep on the move to stay clear. He'll still do the other two eye-beam attacks at different times, so again, stay forward to avoid the sweeping eye beams and move left or right when he raises his head up with eye beams. Use RT + X for the third time, when his health is gone and you're prompted.
After the cut scenes play, you'll get the achievement at the mission results screen.