@ThorM1: Barriers are both lava blocks *and* material blocks. Upgrades do not count as barriers, nor do bugs or lasers (I hit all of these on the run where I got the achievement). I'm not sure about the laser emitters or bug hives, but I dodged those as well.
I found a bug - last champion on level 13, I paused the game (my cat jumped up on my computer) right as the guy was taking his last shots before dying. Unpaused it, and... no death ensues. He doesn't move, the towers don't shoot at him. I can cast spells (though the mana doesn't replenish - didn't notice at first, or I'd've meteored his ass, but I hit frenzy a couple of times too quickly). I can build new towers which also don't shoot.
ARGH, I finally get a brilliant and the damn thing breaks :)
 "Reach the core"){kind=icon}
 "Idle Mine"){kind=icon}
 "Cursed Treasure: Don't Touch My Gems!"){kind=icon}