Does Empowered Ambessa, Respected and Feared attack trigger go through before my opponent's Winds and Ghosts return it to my hand?

Yes, Empwered Ambessa's attack trigger resolves before the opponent can return her with Wind and Ghosts.

Here's why: when Ambessa gains the Attacker designation, her "When I attack" trigger goes on the Chain immediately, creating a Showdown Closed state (Rule 383.4.e.2, FAQ #8384). While the Chain has items on it, only Reaction-speed cards can be played (Rule 354.1). Wind and Ghosts is an Action-speed spell — it cannot be played during Closed State (FAQ #2281).

The opponent cannot interrupt the trigger with Wind and Ghosts. The trigger resolves first, killing an enemy unit. After the Chain empties and Showdown returns to Open, the opponent then gets a window to play Wind and Ghosts as an Action spell — but by that point, Ambessa's attack trigger has already gone through.