For an example three part trial, as it is an example, difficulty isn't scaled properly:
Part 1 would involve getting a number between 1-10 Job Specific Testimonies depending on which equip you are upgrading.
Part 2 would involve fulfilling some objective relevant to the gear, like doing 10000 total damage to undead using banish spells while wearing the White Mage Relic Gloves, or doing 100 Blood Pact: Rage using the Summoner Relic Gloves, or curing 10000 damage with Regen for the Cleric's Briault.
Part 3 would be something along the lines of some challenge NM that you kill a sane amount of times, preferably once, for the trial, such as fighting Fenrir Prime again if your a Summoner, or a Voidwatch NM, or something that is fairly simple to have a clean and easy wrap up to the trail. Should absolutely not have any overlap with Empyrean weapon NMs.
Bonus: Require Job Specific Testimonies to have been consumed in a successful fight against Maat/counterparts for added challenge.