dose ahris legend ability work with empowerd blue mel

Yes — Ahri's legend ability (Nine-Tailed Fox) works normally alongside an Empowered Mel, Newly Awakened. Mel doesn't stop it, and she also doesn't boost it: her empowered "additional -1 might" only replaces events where one of your spells or abilities gives -Might to a unit it chooses (Moonfall/Stupefy style, per FAQ 11740). Nine-Tailed Fox never chooses a unit — each attacker is hit automatically by its own trigger, so the -1 stays -1 (minimum 1 might).

If you actually meant the blue champion Ahri, Inquisitive instead, that's different: she does choose one enemy unit for her -2, so an Empowered Mel would add another -1 there (total -3, still to a minimum of 1). But the legend itself is unaffected.