Here is the full list of all 11 Quantum Protocol achievements.
Clear Ascension 4
Clear Ascension 3
Clear Ascension 2
Clear Ascension 1
Clear Ascension 0
Clear the Dragoon's Comet dungeon.
Clear the Black Anchor dungeon.
Clear the Mirror Net dungeon.
Clear the Neskara Systems dungeon.
Clear the Aegis Industries dungeon.
Clear the Lumei Academy dungeon.