Like collieman says, collecting the extra exp as early as possible is really key.
Here's my (long winded) how I try to do that...
The extra exp comes from chests, the dragon egg, the bombs, and the gnome. The chests and dragon egg are what you will collect in the early game, but the others are also important.
Highest priority is figuring out the board. This is what gives you the best chance of collecting the extra exp. as early as possible. Mark everything you can, crunch the numbers, and use all the tricks. Keep at it until you have the full board figured out.
Pick your fights carefully. In fact, fight as little as possible. Don’t just plow though the monsters because you can. The best game will have the most high power monsters still on the board when you’ve figured out where everything is. Make your picks ones you think will best help figure out more of the board. Lower power monsters let you do more exploration.
Be meticulous with your health. If at all possible, never level up or use a health scroll with any hearts remaining. Plan ahead on your fights to use up all your health, but in a pinch, banging on a wall is better than wasting a heart. It’s one less heart you’ll use at the end.
Find the purple slimes (but don’t fight them), and take out the wizard and reveal all the slimes. The purple slimes are the only 8 power monster, so if you can figure out a tile is 8 or a pair is 16 or a triple is 24 (in the right place), the wizard is within reach.
Find the rat king and reveal all the rats. I find this easier once you’ve revealed the slimes, as it’s the only other 5 power monster.
Find the lich. It’s in one of the corners. It’s important to know where it is before you reach 10 hearts. Kill it as soon as possible and collect all the bomb exp you can.
Keep track of the 4 guardians, purple slimes, lovers, and mimic. The sooner you know where all the high power monsters are, the easier it is to navigate uncertain regions. The race is on to corner the gnome.
Once you’ve figure out the full board, it comes down to carefully killing all the monsters to always use up all your health. Plan ahead. Try to kill the mimic at 11 hearts and dragon at 13 hearts. Similarly, hold off on the lovers as long as you can. Conserving low power monsters makes it easier.
The best I’ve done is 8 hearts remaining.