So, BLUDTUPOWA puzzle: I'm stumped. I've approached this in a number of ways and at this point it appears the solution to the puzzle is either horrifically insidious or it's broken. (for the purposes of this analysis I will be ignoring the first wraith and the two unexplored tiles you must waste when approaching it, since you have no choices in the matter)
I've approached this from a resource-based direction and it looks like there just aren't enough resources to pull it off by any method. I start by examining the boss: 36 HP and physical immune. Since we're restricted to fireballs and cannot progress past level 2, I see two possible attack sequences to beat him (B2P use is presumed):
A) fireball the boss as a 1st level character (+4), detonating another monster with the action and reaching level 2, then fireball him three times (+30), then detonate for the kill (+4)
B) reach level 2, fireball him three times (+27), explore three tiles (-3), then fireball again (+11), then detonate by attacking the dragonspawn (+4)
Essentially these are the most efficient variants of a level-up catapult or regen-fighting approaches against this monster. With no other tools as your disposal, any other attack sequence will just be a variant of these two, and I cannot conceive of a way to improve efficiency.
Please note that if your burning discharges when you level up with approach A, you will come 1 HP short (4 damage + 1 discharge + 27 damage + 3 discharge = 35 HP); option A only works if we can carry our burning between levels. Since the Goat is the only monster that can be killed with a burning discharge, this means we clearly must kill it last with this approach (meaning the Wraith must be killed by means of fireball). Alternately, option B allows us to kill monsters in any order to level up, but we need to have three tiles remaining for the boss fight.
Since the dragonspawn is effectively untouchable a the 1st level, we must clearly kill the other 4 monsters. The Goat clearly must be killed with a fireball and detonate; the Goo Blob requires a grueling three fireballs (just shy a detonate); the goblin requires two attacks or two fireballs (again, just shy a detonate), so we may as well go with two attacks; and the wraith can either be killed with one fireball or one melee attack (6 MP or 3 HP).
If we approach solution A, we need six fireballs (three for the goo, one for the goat, one for the wraith, one for the boss) before leveling up. Since we must avoid mana burn, we have to fireball the wraith. We also need 6 HP to tank the goblin. With the obvious caveat that we cannot consume our last HP, we need 7 HP and 36 MP to pull this off. Since we start with 10 HP, 4 MP, and 13 available tiles, this gives us an availability of 23 HP and 17 MP. We can B2P up to five times for +15 mana. This falls short of the 36 mana needed to pull this off; approach A is clearly infeasible.
So on to solution B. On this side of things, we have to set aside three tiles for the boss fight after we level up. This gives us 10 tiles with which to kill the four weaker monsters; that's a total of 20 HP and 14 MP at our disposal to level-up. This requires three fireballs for the goo blob, and one for the goat. We will use two attacks on the goblin and attack the wraith last and expend 9 HP in the process. Again, with the caveat that we cannot use our last point of HP that means we require 10 HP and 24 MP. This appears to match our resources perfectly; if we convert 10 HP to MP then we have exactly what we need. Of course, there's a problem: B2P can only be used in multiples of three. We will either come up 1 MP short and 2 HP in excess, or 1 HP short and 2 MP in excess.
At this point, I'm completely stumped. As far as I can tell there is no way to get the right amount of resources to pull this off. There just isn't enough available tiles to conceive of doing a level-up catapult, and there is no way to leave sufficient tiles to regen-fight. Does anyone have any other insights or can see an approach that I haven't?