It's a Bug Hunt Trophy

10,000 Xenomorphs (AKA Xenos) is a lot but fortunately they appear en-mass in the majority of the campaign missions and in the Horde, Point Defense and Restock Turrets modes so it shouldn't take that long to grind out this many kills. Depending on how much farming you do for the other misc trophies before committing to the 3 big difficulty trophies, you may well get this early on in the game. If you really want to get this trophy out of the way ASAP, finish the main storyline and unlock the "Horde" and "Restock Turrets" modes then play that over and over until it pops. Notes: You can speed this up by activating any Challenge card that increases the spawn rate of certain Xenomorph types (e.g. They'll Breed, You'll Die). Also, you can check how many kills you have, by looking in the Lifetime Stats menu.