I am not sure whether to separate this into three questions, as it's about three enemy types.
Three enemy types usually spell my doom once I hit around level 13 or 14:
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Spiky: It reflects the exact amount of damage you deal to it. At high levels when the skull has HP over the excess of 100, it's impossible to kill it.
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Rallying: After the board refreshes, converts one sword to skull. If you are unlucky enough to have a board filled with skulls when this boss appears, there's nothing much you can do.
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Flaming: Adjacent squares are set on fire. The flame does tremendous damage for when the skull is at high level.
Are there any ways past those bosses, besides Banish, Teleport or Exorcise?
Best Answer
Spiky: I generally just try to have enough points of Blunting that after a few turns, Spiky has Attack 1, at which point I can poke him to death with several small attacks. The Elf's ability to cut attack in half by Poisoning is good for this too. (Poison hurts Spiky without hurting you, so that's nice, but I haven't found it strong enough to be useful without Elf's extra ability.)
Flaming: The flame only refreshes after you move, not after you use a skill-- so a skill that collects all tokens of a given type (Armour, Treasure, etc.) can collect flaming tokens, leaving safe ones adjacent to the enemy, and a skill that converts tokens is similar. I especially like Dazzle for this.
Rally: Dazzle's good for this too-- you can suddenly do a whole lot of damage at once, and converting all of some other token-type to swords generally connects up the whole board. If you don't have Dazzle, just remember to use the minimum number of swords possible when picking off the skulls that Rally creates. Skills like Armour and Treasure help with this, too, because grabbing a whole bunch of tokens at once will generally (a) compact the board, making it more likely you can hit lots of things with one attack, and (b) bring a bunch of new tokens on the board, some of which will be swords.
I mostly play Raider, Ranger and Mage, with at least two "take all ____" skills (Skill Elixir as one of them if at all possible). Dunno if these strategies work at all for other classes.