After many tries and many hours, I finally finished the second triple quest today! This is definitely the biggest DD challenge I've taken on so far, and I'm interested in discussing it and seeing what strategies other folks chose.
Preps: I prepped the Balanced Dagger. This item is a big boon, especially since it's small and 2-1 lets you fill your inventory with helpful small items. I had prepped Dragon Seal in the past, as I did for Triple Quest 1, but ultimately I think being able to save blackspace and resources by fighting equal-level monsters is the way to go. Potions were Reflex/Dodge/Schadenfreude/Whupaz, since if 2-1 goes well I should only need one burn salve. My other preps were Shop Scroll, Mystera, Perseverance Badge, Magnet:Fireball, Smuggler's Den, and Translocation Seal.
2-1: The Shop Scroll turned up the Battlemage Ring, which I burned Translocation on immediately since my preferred way to get through this level is to lean on Fireball as much as possible. WONAFYT showed up quickly, which is of course very handy with the Balanced Dagger. BLUDTOPOWA didn't show up, which would have made things very easy, but I was able to get up to level 8 taking minimal corrosion, relying mostly on fireballs and a courage juice. I bought a Soul Orb, which I knew would be great in 2-2. APHEELSIK, regen fighting, and the level 7-8 ding made the boss go down without having to burn any resources. I proceeded to 2-2 with BURNDAYRAZ, WONAFYT, the Battlemage Ring, and a bunch of small items including one slot of attack-boosting trinkets.
2-2: Is there a way to beat the boss of this level that isn't a WHUPAZ strike followed by breaking all three totems? If so, please let me know, because nothing else ever got me anywhere near. I found HALPMEH lying around and converted the Battlemage Ring. The Soul Orb to prevent mana burn plus HALPMEH to clear poison made the monsters pretty manageable. (The trinkets from 2-1 are also handy. Before I started prepping the Balanced Dagger, I was usually able to take on stronger creatures and use levelups to cleanse.) I bought the Venom Dagger, which is not fantastic but handy and small. I found and worshiped JJ at level 3, which is later than I prefer of course, but it worked out OK. The only boons I used were Petition and Chaos Avatar. I used courage juice to get almost to level 8, used WHUPAZ and broke the totems, dinged 8, used up my health and mana, took Chaos Avatar, and then used regen fighting to finish off the boss without having to use any potions. Then--and I'm proud of this maneuver since I don't usually mess with conversion antics--I desecrated Dracul so I could convert into Tikki Tooki; then I killed some popcorn and desecrated JJ for two shots of Reflexes to take into 2-3. I also converted HALPMEH and picked up CYDSTEPP at the very end, since 2-3 seems pretty hopeless without CYDSTEPP.
2-3: I was feeling good entering this level with 3 each of Reflexes and Dodge potions and 11 mana potions. I had only been to this level once before, and the previous time I didn't run out of resources, but I ran out of usable resources--a bunch of health potions remaining but no way to take a single hit. My luck turned a little bit against me--I didn't find the Orb of Lusory until late and the high-level monsters weren't manageable (Illusions, Goo Blobs, etc.) so I had to summon the bosses at only level 8. Learning my lesson from the last time, I used my health potions on the warlock and wraith bosses before ditching Lusory to buy a Crystal Ball. It turns out that wasn't needed because my three shots of Dodge/Reflexes and giant pile of mana potions were more than enough, even to punch through the horrifyingly tough goblin boss.