YOU CAN GET THE ACHIEVEMENT ON THE XBOX ONE EVEN IF YOU GOT IT ON THE 360, but it is going to be a PAIN IN THE A**! You have to go to local. In local, none of your leaderboards transfer over, but you can still get achievements. To get the achievement for escaping the 1st time on xbox one, even if you got it on xbox 360, you have to beat a game in LOCAL. Now, here is where it gets hard. In local, you will be a level 1 no prestige. No sentry guns, no explosive ammo, no full auto pistol, nothing. You get all the stuff you would normally get at level 1. You can split screen with a friend at your house, but that's it. You will most likely have to go solo it, but soloing extinction as a level 1 is damn near impossible. I made it to the nuke, armed it and died on the way back.(And no, the glitch for jumping off the map to make none of the meteors show up does not work on solo.) The best option if you really want to get this achievement is to play multiple games in local without leaving local. As local does not save anything you do once you leave it, you can play multiple games to get to the level(and gear) you want and then try to escape, but that will require at least 4-5 games in a row. If you REALLY want that achievement, this is you only option until they fix the achievement. Hope I helped. If you have any questions, ask and I will reply to them as fast as I can.
also since they will be doing double xp for extinction this weekend, then it may level you up faster in local play extinction and you may be able to get everything you want to unlock faster.
also some people may ask what glitch am I talking about. I will explain it to you. Say for example you have 4 people in an Extinction game. When you get to the part where you arm the nuke and the meteors fall and block your path, you can make both of the meteors not fall. All you do is arm the nuke and have one player walk off the edge at the nuke and die. then about 50 feet to the right(up on the hill next to the really high porch) his dog tag will appear and you go revive him(i suggest have the medic revive him). Then I swear to you it is a straight shot to the helicopter with no stops along the way. Makes the ending very easy.