Probably not even that hard (if you start with enough gold/altar... but then resistance, not sure), but the time limit makes it challenging I suppose:

Start as Chaos Knight and save the puppy (no wishing).

Obvious tactic: start with money talents, hope for altar, change to N to get the quest, then back to C to stop dying and dive for the puppy. If quick enough there is plenty of time then to get resistance (or does puppy still have food clock if dropped at other dungeon?) for the closure (if at all needed, maybe candle troll can skip this altogether if quest succeeds even without talking to girl, no idea), few unknowns here, but should be doable.
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