• Set autorun on in the gameplay options (or use the run key almost every time, your choice).
  
• Start a new game on a lower difficulty and hit "Trust no one (demo)" - play it 2-3 times, until you know where you have to go and what you must and mustn't do. The achievement requires you to do the same in Bloodbath difficulty.
  
• Use your save and load skills often - it doesn't matter how many times you reload, the mission timer counts. If you do it right and fast, you should finish the demo in 5 minutes.

Actually, the starting place is right away the hardest part of the achievement, you will die probably
several times while trying to get out of even the first door. The problem is, there are 3 guards you have to kill with your punch dagger and there are almost no health items or armors to support that. Bloodbath makes the guards go and shoot faster and you will die in seconds. But don't give up!

The tactic is to line up the two guards somehow while hitting one of them (for example run immediately behind the pipes to your right, but can be done otherwise also). It's very important, because one guard will shoot the other in the back and help you kill him. If you managed to kill them with about 50 health remaining, save the game. Open the door and punch the third guard to death. Probably you will have about 10 health remaining. More is better - if you have such low health, you cannot run, so use a health item as fast as you can.

Go talk to Harris, grab all his stuff. The gate opens only when you finished the dialogue. He gives you a crossbow. Of course, don't use that while in town... yet.

Before the action, we need some important items.

Go to the back of the smith's house ("Armory"), jump into the chimney...

...grab all the stuff inside,especially the leather armor. Use the lift at the end of the room...

...and grab all the stuff in the upper room. The poison bolts are critically important! Break the window and jump out.

Don't forget to go to the hospital too, grab the free med patch and buy a field surgery kit. Run back to the entrance of the Sanctuary.

The door is locked so use the alternative route by the river and grab the stuff while continuing forward.

After opening the door, just run to the lift (grab the items).

Kill the two guards up there (you can use the lift as a cover, simply push the button again if it goes down). It's better to use only the electric bolts yet, as the guards in Sanctuary are easy to kill.

Follow the corridor, turn left, grab all the stuff at the wall...

...kill the guard, use the switch to open the bars.

Go back, kill the two guards and move on. Turn the switch to activate the bridge...

...jump into the water and use the switch on the side of the bridge to lower it (faster than running back).

Kill the two guards waiting at the top of the lift then turn left, enter the room.

Kill the red guard, pick up the key and grab all the stuff, especially the metal armor!

Run back across the bridge again, up the lift and enter the small room next to the force field. Use the switch to turn the force field off, grab all the stuff.

Now you can pick up that fancy cup! Go back to town.

It's a setup, they are waiting for you. You must act quick here or you will be overwhelmed, so use
your poison bolts now, it kills the guards in one hit. (Don't try to drop the chalice, the guards won't attack you, but you won't be able to enter Harris' room.)

Enter the room, talk to Harris again, choose to keep the chalice. Kill him and use the switch to enter the small hidden room, grab all the stuff there.

Blackbird starts to speak to you and tells you to drop the chalice. Fight your way out of the tavern and drop that cursed thing.

Out of the tavern turn left and enter the mansion of the governor. (If you still have the chalice, the alarm goes off and you will be in trouble.) Use your poison bolts and kill all the guards while
entering the building.

Turn left, go down the stairs and grab everything you can, espcially the flamethrower and the shadow armor. Activate it while fighting your way out.

IMPORTANT: If you killed every guard with poison bolts, the Crusader robots will not spawn outside and you won't be able to advance in the game, so use your flamethrower at least once while running out!

Kill the three robots with the flamethrower (it's easier than you think) and pretty much everyone in your way.

The door to the teleporters will open at the back of the weapons dealer's house (next to the smith's house). Enter the teleport.

Step out of the teleport, go talk to Macil - the door behind you will open only if you finish the dialogue.

Go through the door, follow the corridor and use the end switch.

If you managed to do all this under 6 minutes the achievement will pop up. Congratulations!