Maid of Sker

This will be the hardest achievement in the Challenge DLC. It's a big step up in difficulty since the enemies here are damage sponges and hit like trucks.

Basic A* requirements for the other challenges are no deaths, ~100 kills, and finish in under 20 minutes. This challenge has a lot more leniency with kills, otherwise you'd never get done in the required time. In the video above, I get the A* rank with 46 kills and finish in just under 20 minutes. These were my stats in my initial completion.

You should have completed the other challenges and know your way around the mansion before even attempting this one. In order to get the A* here, you'll end up fighting through enemies in the early areas, then running past everything to the boss. You need to move quickly and grab ammo and healing jugs on the way.

The best way to deal with normal enemies is to rifle headshot them, then when they charge, finish them with an axe swing. If there are two or more hostile at once, you can't really engage them and will need to run, either past them or backwards far enough to hopefully create distance.

Helmeted enemies can be killed with four rifle body shots. Don't even bother fighting the invisible/ghost enemies, the fat fire guys, or the crazy teleporting women.

There are a few safe places (elevators, crawlspaces) where enemies can't get to you and you can safely kill them. This allows you to rack up some easy kills from safety.

Always have your guns loaded, especially the shotgun which you'll want to use in a pinch if your path is blocked as you're running through an area.

For the boss, you want to keep distance, shoot him when it's safe (ideally with the shotgun), and always focus attention on the two normal enemies when they spawn. I believe they come in three waves of two but more may spawn if you take too long.

It'll probably take some practice to work out the kinks and not get unlucky with bad enemy spawns. Good luck.

vSully's guide is awesome. Read his advices and watch his video.
As he says you really should know your way around well, and maybe throw in some further exploration in a couple of rooms he does not cover because he doesn't need an extra drink or some extra ammo.

But I just want to add one thing: this DLC is kinda broken. Some bug I encountered on my way to getting this painful achievement:

1 - When you shoot / swing your axe crouched in a vent, sometimes the hit won't register. So you just end up losing time swinging eternally, and the enemy does not die. It happened to me especially with the invisible bastards.

2 - Enemy spawns are predictable after you play for a while (i guess there are only 2 or 3 main scenarios); but don't ever get your guard down, because so many things can go terribly wrong. Like headshots not registering, or shooting an enemy and bothering 2 or more that come for you at the same time. You can - most of the time - lose them if you keep running, but their determination in chasing you is completely random. Don't - i repeat don't - save bullets. You will have plenty of bullets by the time you get to the boss. So use those weapons, and try not to put your bullets in the wall because it will affect your accuracy of course.

3 - When you start running and you end up in those tiny corridors through the walls, pay attention to how many enemies are following you. The game likes to put an invisible guy or a laser guy right in front of you, and you cannot avoid them. If you get stuck with enemies in front and behind you, you're dead. So consider the option to clear some rooms before entering the tiny corridors. Especially if you just have to deal with a laser guy: they're slow and go down with 4 rifle shots (well, sometimes. Some other times the game decides you need a lot more bullets. But it's the game, it's not you).

4 - I'm pretty sure you need to get 100.000 points for an A* grade. The first time I finished this stage I had 99.210, and got an A. It is unclear what you need to do to get an A*: I guess beating the stage in 20 minutes is mandatory. But you also need to kill enemies and not get hit too much. Trust me, you will know that you did a good run when you get to the end after trying this 10/15 times like me.

All in all, it takes practice. But it also takes LUCK. It's not just skill. So don't get too discouraged, don't rage. Take it easy, and sooner or later you will get this.