Use your first strike, fireballs and your enhanced evasion to take on high level monsters early on and preserve your potions for boss battles. Be cautious though, since monsters with first strike still have priority, no matter the level.
If you're stuck in a no-win scenario, go for a desperation strike against the toughest thing (that doesn't have first strike) you can two-shot. You just might get lucky and dodge their attack enough to explore more or gain a level.
Race and Deity Choices
Dwarf is an obvious choice for a Rogue to make up for his lack of health (otherwise stronger opponents will wipe the floor with you). If you're cocky, Human, Gnome and Orc are still solid choices.
While rogues can gain piety easily for Tikki Tooki, they can't make much use of his boons, and they stand to lose a LOT if their piety dips below zero. You don't want to waste your first strike by converting to Mystera Annur or Jehora Jeheyu, either. The other gods are all fair game, though.
Not that much of a challenge here. Take on high level Serpents and Nagas with fireballs and melee attacks to level up. Be careful with Gorgons, since they have First Attack themselves and will always attack you first in melee, no matter your level. Use your piled up potions and midfight level ups to take on bosses and take care to not get petrified or poisoned.
This can be a little annoying, but not too hard. If you get the Glowing Guardian, it will be a bit easier. Without him it can get a bit tricky to beat the bosses. Just make sure to quickly hit level 7, so you have enough spare monsters to level up midfight. First take on the Tormented One, as he is the bigger pest. Attack him until you're almost dead, level up and finish him off (use Mana Potions or another level up, if needed/possible). Afterwards Frank can be outstalled with Potions. Always have an eye on your HP, since they deplete relatively fast.
Basically the same as in the Snake Pit. Difference is, that there is nobody to poison, petrify, weaken or first strike you. With fireballs you can easily take on Dragonspawns two levels above you. Imps are easy to battle, too, but can often be annoying, because of Blink. You have to be careful with the bosses though, since they are a little stronger than in the Pit. Saving potions and/or magic resistance can help here.
The Rogue's low health really hurts in this dungeon. Most of the enemies here will one-shot you if you're not careful or very lucky. While the BURNDAYRAZ glyph is the most mana-efficient way to whittle down Animated Armour to power-level and set up mid-fight level-ups, you may find that CYDSTEPP is more useful overall. APHEELSIK really only helps against the Meat man enemies, as the Golems are quite likely to resist it. (Note that poisonous melee attacks will bypass magic resistance, however.) If you find CYDSTEPP you can take down Iron Man fairly early; otherwise go after Super Meat man first.