I've played these missions a thousand times and Karma (Chloe) survives. But when I play Odysseus, it still says that the Obama was lost and the trophy doesn't pop up.
1) Let DeFalco Escape
2) Play Second Chance; rescue Karma
3) Choose to kill Harper
4) Injure Briggs by shooting him in the leg.
I did all the steps exactly 5 times and it still will not work. I'm tired of rewinding the story.