Unholy Traveler
Medium-short challenge: ~30-50 minutes at 1e151 mysteries, depending on attributes and items
(not sure what time those challenges were updated but as of 31.08.2023 this challenge takes around 5-10 minutes with 500 attribute points and 9.12e178 mysteries and no items)
Strategy
The idea here is to generate and use compressed time as quickly as possible. The generation part is easy: put a lot of attribute points in Wisdom, and set 
Singularity Beam on reckless autocast. Of the spells that use compressed time, 
Wormhole, 
Stabilize the Flow, and 
Time Helix will all reset your progress, so you primarily want to use 
Temporal Distortion. Add in 
Generate Paradox if you end up building up compressed time faster than Temporal Distortion can consume it.
Upon starting out, use a Wormhole/Singularity Beam loop to level quickly with 
Conjure Manabeast and 
Synthetic Entity. Then turn off Wormhole and set the following on reckless:
- Singularity Beam
- Conjure Manabeast
- Temporal Distortion
Ritual Of Power
Converge Timelines
Superposition
Buy mana sources and upgrades, and wait for your pet to reach level 100. Once you have all the upgrades that you're likely to get, you can turn off the three incantation spells to get more Singularity Beam casts. (Though this might not matter if your Singularity Beam cast speed is limited by frames rather than spell shards.)
Suggested attributes:
- Wisdom 150
- Mastery 25
- Whatever attributes are needed for useful gear (see below)
- ~Spellcraft
- ~Patience
- ~Intelligence
Suggested items:
- Stabilizing Pauldrons
- Pet exp% boosting gear
- Wisdom boosting gear (e.g. Easymind Hat)
- Whatever will boost profits the most (e.g. incantation efficiency)
Note that Clockcarers are pretty useless (unless used for a set bonus), since as usual for the Chronomancer, the main source of compressed time is Singularity Beam.
(Open question: Does a buff to non-% pet exp help? E.g. the second set bonus from the Falconer's Trust item set, which increases bonus pet exp by 100.)