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