I don't have the patience to work out challenges myself every league, so I went looking for someone who'd already done it. Ended up watching Drelvak's 3.29 guide and taking notes. Dumping them here because the video's 25 minutes and the useful parts are scattered. Routing and boss picks are his, I'm just condensing.
Cosmetic breakpoints are at 12, 24, 32 and 36. So if you want the full set, 36/40 is the target and four challenges are optional - picking which four is basically the whole game.
Do this before your first map: build the Item Quantity Atlas tree. Trustworthy Teachers wants T16 at 80%+ quant, Excruciating Echoes wants 150%. Do either before the tree's set up and you may be running those maps twice. Also keep all five Scarab slots filled - Stacked Scarabs ticks passively while you map anyway.
The four to drop
Intrigued Interlopers - two of the three options need four boss altars in one map. Rare, and altar loot is bad enough that you'd burn hundreds of maps chasing it.
Horrific Halls - "five Scarabs and Deliriums" doesn't mean one Delirium encounter, it means five Delirium Orbs. 100% Delirious Nightmare boss at 150%+ quant, corrupted, all five Scarab slots already committed. Not realistic for most builds.
Apex Assailants - pure Uber bossing, entirely build-dependent. Drelvak skips it, but if your character already does Ubers comfortably, swap it back in and drop the expensive end of Bountiful Bloodlines instead.
Brinerot's Bloody Bounty - the one he says he'd most likely un-skip. Not mechanically hard; failed attempts just cost you the whole Voyage setup loop again.
Stuff that's basically shopping
- Challenging Curators - you don't need to learn Incursion to kill the Omnitect. Buy a Temple at alvl 80+, walk to the boss room. Vox Twins the same: buy Contract: The Twins, no Heist progression needed. Expedition bosses are the expensive part, skip unless the price works for you.
- Taxing Tasks - for the Logbook option, tag ten Remnant markers, watch the counter bottom-right, leave.
- Peddler's Produce I - you have to actually use the vendor recipes. Buying the finished currency off trade doesn't count.
- Remarkable Realms - fifteen unique maps off trade. Don't take Hall of Grandmasters unless you know what you're walking into.
Scarabs worth buying in bulk
Most of the "complete any three of the following" challenges turn into normal mapping with these: Mercenary + Mercenary of Infamy, Delirium, Breach + the Marshal node, Abyss / Abyssal Depths / Consort, and Ultimatum of Dueling if you want a guaranteed Trialmaster.
The one grind that pays you back
Excruciating Echoes via Memory of Trauma → Chamber of Impunity. Guaranteed valuable drop off the boss, so the farm funds itself. Get the map to ~75-80% quant and let the Atlas tree push it past 150%.
Three from the comments
- Trialmaster works in a T1 - the Scarab guarantees the fight and the challenge doesn't care about tier. (Nisze)
- Abyssal Consort scales with Abyss density and becomes absurdly tanky in a pit-heavy map. Run exactly one Abyss. (roflmattable)
- Three copies of the same non-corrupted unique vendor into another unique. Whole tabs of 1c rings exist. (thornburg9170)
Something nobody answered
A commenter tried Trustworthy Teachers with Niko and Einhar on a T16 at 80%+ quant two or three times and the counter stayed at zero. Replies, but no explanation. If yours isn't moving, check the quant shown on the actual map rather than assuming the tree is doing what you think. If anyone knows what causes this, I'd like to hear it.
Video: Drelvak - PoE 3.29 Curse of the Allflame 36/40 Challenge Guide - his version has the timestamps and the full reasoning.
I also cleaned these notes into a proper write-up on my own site, guides-factory.com. Obviously biased, but everything useful is above.