Something like a file at .minecraft/config/advancementinfo.json which could then be formatted like this:

{
  "advancement_internal_name_1": {
    "advancement_criteria_internal_name1": "Text 1 to replace with.",
    "advancement_criteria_internal_name2": "Text 2 to replace with.",
    "advancement_criteria_internal_name3": "Text 3 to replace with."
    ...
  },
  "advancement_internal_name_2": {
    "advancement_criteria_internal_name1": "Text 4 to replace with.",
    "advancement_criteria_internal_name2": "Text 5 to replace with."
    ...
  }
}

Example:

{
  "husbandry/wax_on": {
    "wax_on": "Use honeycomb on copper block."
  }
}

The above would take the Wax On advancement and replace the wax_on criteria of it with Use honeycomb on copper block on AdvancementInfo's in-game sidebar.

The "namespacing" within advancements is for incase of 2 advancements sharing the same criteria, but you want to give them different overrides.

Of course it doesn't have to be a JSON file, YAML or any other format of preference would work, but JSON would be my personal pick :P

Datapack and mods support

When declaring an advancement in the JSON file, just assume the minecraft: prefix if there is no prefix, then datapack/mod advancements can be achieved by using their prefix.

#16 (comment)

well fair enough nevermind then