It's possible to navigate the entire vault and not be forced into combat. You just have to be very stealthy and heed the new enemy footstep indicators. They are key. You will see their footsteps as little shadowy water rippling looking things in the darkness.

Don't explore new rooms by just turning a sharp corner where you might stumble into a sleeping enemy. Try to keep some distance and go wide around corners.

Enemies can't see behind themselves, only in front. This is different from the normal game. Before you just barge into a door, pass a few turns to see if there are footsteps of an enemy right on the other side. If you do see footsteps on the other side of a door, wait until the footsteps are going away from you, you can open the door and the enemy won't see you, and you can even follow them as long as you're not too close. But sometimes they do spontaneously turn around. Even then, they don't immediately see you. They turn into investigation mode. And if you run away in the opposite direction, back to the previous room, they often will not follow you because they were looking for the source of the sound where they started to notice you.

There is also the standard way of losing enemies in the game. If you walk around a single square of wall or untrampled grass multiple times, the enemy will lose track of you, and if you time it right, you can often walk straight away from whatever thing concealed you, and they will randomly go the other direction.

None of the enemies in the vault wander from their prescribed pattern unless they're chasing you, so you will never have an enemy randomly opening a door. So you only have to worry about dodging the vision of the enemies in the room you're in.

Only some enemies patrol their room, and their rooms are usually designed that you can avoid being seen by them without too much effort. However, it might require lots of walking back and forth until the timing seems right to go out a new doorway.

If you just can't lose an enemy, like they are right on your butt, and there are no single tile features to run around, that's when you have to use one of those two teleport crystals you find in the starting room. They take you back there. Obviously, make sure you don't use one while you're in the starting room or it won't help at all.

Many enemies are sleeping and sometimes guarding treasure. You can often wake those enemies up and have them chase you widely around the room while you loop back and open the treasure to see what it is, then lose them, and do it again until you can get to the treasure without being hit as you pick up the item.

The other idea is to find a room that only has hazards with no enemies. Some of them require you to avoid hazards in a pattern to get whatever item it is in there. Whereas other hazard rooms are like the puzzle rooms in the rest of the game which can't be solved without a specific item, unless you're OK with taking damage. (There's one room I still can't figure out how to do without taking damage.)

Once you find a +2 or +3 weapon, and at least some armor, you can just kill most enemies. All the normal tricks apply with softening them up first with ranged weapons, plants, stones, potions or whatever.

As far as I can tell, things like a Potion of Liquid Fire is not particularly good against the final boss. This is actually surprising, which you will understand when you finally face them. So don't be afraid to use any you find on particularly difficult enemies. The same is true with plants, you can throw seeds of dangerous plants where an enemy will step.

Some enemies are a lot easier to kill than others, and those should be the ones you kill first, especially if they are guarding treasure chests.

There's really no reason to ever die in the vault unless you're really pressing your luck in a fight. You start the vault with a crystal that teleports you out of it completely. You won't get any reward, but you won't lose anything either.