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As someone who has switched characters a few times. I definitely know of methods to get around it. 

With Grant, getting battle hunger is his saving grace, as once he gets to a point he can one-shot enemies, he can infinitely stack atk using his skill. Only problem coming from it being exclusive to the caves and enemies having magic shield or revives. He lives through being able to buff his attacks to obscene amounts, so acid and boulders are to be avoidd at all cost. His special is good if you're surrounded by tough enemies you might not be able to one-shot, or to destroy things like boulders or acid.

With Jin, It's a bit harder. I don't really play him much, just did it for the achievement, but It's best with Jin to sit in a corner the whole time and take potshots at enemies. To keep him optimal requires guzzling so much mana you'd think he'd be a mage, but typically save side strikes for if you're surrounded by enemies, and pick up mana whenever possible, and relics that increase max mana (yes even the topaz) are viable.

Lily suffers from a lack in health increase the most, as her main skill is being able to hurt enemies with healing, and most her builds revolve around her being a tank, soaking dmg to then heal it back and harm enemies. For her, dragons blood upgrades are a must, and the sprout upgrade is almost essential. Keep an eye out for medics and try to get the most out of them for free health, potions are generally meh, and try to avoid enemies like gnolls and vipers. her special is really only useful in the desert where everything can revive at least four times in late game.

EDIT: another thing I just wanted to say about Lily is what a PAIN it is to complete her achievement. Dealing 12 dmg with one instance of her passive is impossible without the help of dragons blood, so you need to be lucky enough to get to tier three dragon's blood, and then get down to one hp without getting murdered beforehand.

Zovac, like Lily, suffers hard. As Zovac, you spend the whole time trying to line up weak enemies (or ones manually withered to one or two hp) and poisoning them, chaining destruction bound to destroy any enemy. The problem comes from the fact that poison takes a long time to kill enemies, and it only gets worse as they get more health than lily drugged on a max dragon blood artifact, so you need ways to waste turns. Zovac has one of the best specials in the game, doubling dmg from EVERYTHING, so in late game, you'll tend to stray away from poison for the most part and spam your special once spear traps or bombs come into play. He also has a good skill that wastes turns and nullifies poison from poison shrooms and vipers while healing, a good skill to use if low, or need to waste turns, and definitely use it after being hit with poison.

Like Jin, I only played Drex for the achievement. Drex is odd, he's like the hammertime of the characters. stacking sand shields he uses in every one of his abilities. His runic tombstone is extremely situational, his dust burst is really only good for adding onto extra hammertime shenanigans, and his sandstorm is really only good for getting out of a tight spot, as the dmg of it, like firestorm, becomes obsolete in late game. Relics that decrease his chance of being hit, or lessen dmg from a hit like the novice shield or dwarven helm are ideal, as players that use him don't ever wanna get hit, and wanna take minimum dmg when they do.