EDIT 9/9/2015: People are reporting that these achievements are now unlocking normally!
This is a possible solution to unlocking both this achievement and Don't Panic if they are glitched for you. As a heads up, this will only work if you have a physical copy of the game because it relies on being able to play without the patch being installed.
1. Disconnect from the internet and delete your save data. Make sure to select "only delete from console" if you want to be able to keep your saves.
2. Delete the game and DLC. You don't have to delete anything Gat Out Of Hell related.
3. Re-install the game. Make sure you are still disconnected from the internet and do not install the patch.
4. Play through the game until you complete the missions that the achievements have glitched for you. I would recommend playing slightly farther just to make sure you pass the point where the achievement would normally unlock.
5. Save the game and then hit the home button and quit from the main dash.
6. Reconnect to the internet and download the update for the game.
During the update the achievements should pop. They probably won't pop together and probably wont pop right at the beginning of the update. For me they popped about a minute apart or so after the download hit 3% but it might take a longer or shorter time.
Huge shout out to "Monty BUCS FAN" over at xboxachievements.com who is the person I got the method from.