I beat all of the fights except for the final boss fight on my first attempt (I got bad luck in my rolls in that fight, and needed a second attempt to win).
The most powerful mechanic that you have at your disposal is the ability to parry; doing so smartly allows you to effectively multiply the impact of your own dice. It's frequently worth it to spend a turn or two intentionally tanking hits from your opponent (blocking only what's necessary to survive if needed) so that you can gain an advantage in stashed dice; after that, you can parry by matching your opponent's attack exactly and then use your accumulated reservoir to overwhelm your opponent's attack for a game-ending swing on the turn after that.
I used the +2 to die, flip a die, deal 3 damage/turn, and draw +1 die/turn for -10 starting HP artifacts, all of which contribute to being able to build up a valuable pool of dice. Note that the +2 to die and flip a die artifacts combo well with each other: adding 2 to a 5 die will turn it into a 6 die and a 1 die, and adding 2 to a 6 die will generate a new 2 die; meanwhile, flipping a 1 die produces a 6, and flipping a 2 die produces a 5.
I beat the crane and croc duo this way before the croc even had a chance to fire off his debuff.
