My thoughts:

The ultimate goal is to kill the dragon, which has 15 lvl, so you need 15 hp (15 lvl) to fight it.

You therefore need to get 15 lvl.

You therefore need to kill monsters.

Killing monsters doesn't give you enough exp, so you need to find healing/gold to compensate.

As you pointed out, healing scrolls heal you completely and therefore are more effective at higher lvl.

The strategy therefore, is to search the map for gold and healing, by spending as few health as possible.

The exception from this strategy, as pointed below, is gaining information (helping in the above strategy) by killing the slime mage and rat king.

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My tips:

- if you can't find a low lvl monster before healing up, hit a wall to get your hp to 0. I think a wall on average gives you less than 3 gold, which makes it a punishment for when you didn't strategize the monster killing optimally. Of course the wall could be strategically placed, explained later.

- Prioritize hitting low lvl monsters above hitting high lvl monsters, because you want to explore as cheaply as possible.

- Prioritize hitting where a monster can be, above where it surely is. It's probably a good idea to decide where to click based on average possible lvl multiplied by the chance it is there. Calculating this could be extremely hard (it would involve statistics from the Monsternomicon for example) but estimating it is pretty simple. Obviously ask yourself a question if you want to risk death if the average is very attractive, but maximum is beyond your current hp.

- Prioritize revealing fields with possibility of monsters of the category that you almost entirely discovered; you want to remove that lvl from possible combinations. Doesn't apply to rats and slimes.

- Of course combine the three points above with prioritizing fields that give you a strategic advantage; it's tricky to explain what a strategic advantage is: for example being able to swipe from a side, so that you have two numbers, where one describes 2 fields, and other 3, so that you can derive the strength of the third...

- SUPER IMPORTANT: try to find the slime mage: the pattern is simple, he's only lvl 1 and you want to kill him as early as possible.

- IMPORTANT: likewise, you want to kill the rat king as early as possible. That's the only non-slime 5, so should be easy if you listened to the above point.

- 3-digit numbers can be thought of as two numbers XYY, where X is the number of mines, and YY is the sum of strength of monsters. The game then plays as Mamono Sweeper (BLIND mode) merged with minesweeper, you can separately try to figure where mines are and the monster distribution. The logic of both games then applies.

- Just like you know the first digit of a 3-digit number must be a number of mines, because monsters aren't strong enough to combine to 100, sometimes you can know the distribution of monsters based on possible combinations. In particular, you should be able to quickly rule out all lvl 5 monsters, and all lvl 8 monsters, so you're left with a just a few lvl 6-7. You will probably save yourself a lot of time if you don't miss the moment when all lvl 7s are revealed. I think lvl 11 hides near eyes, but lvl 10 should be easily found. Rat king rules out lvl 1, so if you hunt for bats, the number of combinations becomes very manageable.

- Once on lvl 11, you probably already won. This is the time to kill the lvl 11 guy. Before you do this, mark your mines.

- Reveal destroyed mines. No need to remove the mark.

- Spot patterns, as Monsternomicon suggests. The most important is the fuchsia slimes pattern, also lvl4 go in vertical/horizontal pairs - near the end of the game you probably can figure out where the pairs are based on detecting x+y = 8 strength, and limited number of positions where the pairs could hide.

- I didn't dare to kill the mimic, because Monsteronomicon told me to fear it.

At the end, by using the strategies described above, I killed the dragon with 3 healing scrolls left: https://i.imgur.com/0Iz2IqT.png