Your mod is kind of in the ballpark for something like this so I thought I'd ask.

The ability to have a command executed when an advancement is made.

LootTweaker is for modifying loot tables using ZenScript. Advancements are a completely different, unrelated system and therefore this is out of scope for LootTweaker. Also completely unnecessary as vanilla can do that anyway. Advancements can run functions, as detailed here.