Remember you can kill multiple enemies in a single move if they are in the right place.
Get surrounded
If you're smart with your dash moves, you can take out multiple enemies by jumping to a square. If there are multiple enemies around you when you land, so long as they're in range of your knife, you'll stab them all. On the flip side of that, getting surrounded in normal play is a terrible idea. You can only attack after a move, so if there are enemies around you, you're going to have to move away and then back in to attack them. That leaves you open to getting shot. A lot.
Heal
Do not forget to heal.
Healing takes a turn
Healing is an essential part of the game, but remember that it takes a turn. That means while you're glugging a potion, all the bad guys on a level are going to move. This can put you in real jeopardy if you're not careful. A good way to protect against this is to concentrate on upgrading your healing abilities on the first few turns. Up the number of hearts you've got, and get the boost that means healing potions are more effective.
Line them up
Because you only have a small amount of bullets, you want to make sure they do as much damage as possible. There are a couple of ways to do this. You can move your enemies so two or more of them are around the red barrel. When you shoot this, it'll do damage to anyone in the adjacent squares. You can also shoot through enemies. If there are two bad guys in a line, shoot the one at the back and the bullet will travel through the bandit in front, killing them both.
Refill potions
Heal before you refill your potions to get a better return.
Think ahead
You know how your foes move, and you know where they can hurt you. Using this information you can usually work out where they're going to go next. Predicting what the enemy is going to do is key to success. Watch their patterns and get yourself in a position where you can't take damage, but you're perfectly poised to strike when the time is right. See, it is like chess.
Work on your upgrades
In the first few levels, try not to get hit or use any of your special moves. This way you can focus on upgrading your attacks and healing powers for when you need them. It might be easier to shoot your way out of a level, but playing smart will set you up for later in your run. Make your shots longer, make your dash go farther, and when there are more enemies on the screen you're going to be in a much better position to take them down without dying.
Enemies...