Charred scar isn't really hard at all, per se. You can fail the count down just fine, it just effects some of the stuff during the remainder of the game. Stuff in the way isn't too big of a deal... usually the worst of it is maybe some fire wyrms. S'mostly just hatchlings with the occasional drake, though, iirc, and a smattering of other junk. Elementals, maybe the odd demon.
... that said, it does look like it's somewhat unlikely you'd manage to beat the timer as is. Controlled PD'll help a little, but you've got no movement speed boosters at all (why no essence of speed?), movement infusion or otherwise. You'd probably be fine if you cobbled together all the passive movespeed kit you can* (Dunno if you've been doing it, but I tend to keep stuff like that laying around the fortress storage, just in case) and spammed the CPD, but yeah. Movement infusion would make things more likely, at least.
*You've got boots of speed, which is good. Giving the shops a look to see if they've got nimble leather armor (or if you've got that early game water robe still laying around) and any ms boosting jewelry (Happen to have found and kept feathersteel amulet?) might be an option.
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Not sure if I'd go with unbreakable will... are you actually having problems with mental effects? Could you go with draconic will instead? Not passive, but more versatile. Roughly the same with cauterize... do you need more defense or more offense? I tend to prioritize the latter, m'self, and you've already got a defensive prodigy. If you have access to meteoric crash, I'd probably recommend that. Eye of the tiger could also be good for an archmage, especially since your crit is already up there. Elemental surge would be fine, too... especially with that arcane focus, another 20% casting speed reduction would give you some hella' dakka, though meteoric crash would probably give even more.
And yeah, for a mage in the final battle you kinda' just pop shields and nuke everything into the ground, s'far as I can remember. Maybe bounce around with CPD and probability travel (if you bother to get it, anyway. Might not be an issue with quicken spells dropping the phase door cooldown.) if you need some room.