Friend of the Aluxi

The Aluxian Resurgence are one of the minor factions. Rep can be increased by spending influence points with them using the minor factions menu at the top of the screen. The max rep costs 6 points so you'll need 13 points total to reach max level.

It doesn't really matter whether you're friendly or fighting with them whilst you do this - you can still increase rep to max and pop the achievement even when battling them.

And, after reaching max rep, there's A Doomed Dynasty to kill them all off afterwards - but aim for Peacemaker (max rep with all 5 minor factions) first..

This achievement is soft-missable because if you obliterate them first (or another faction does!), then its no longer possible to reach max reputation level with them in the same match.