Gamer has been removed
I have created a gametype for this achievement. It is called "Skirmishers/Invulnerable Boost".
You can use it for both this achievement and for farming Skirmisher kills.
In this gametype, you are invulnerable and you deal increased damage.
I suggest using the Firefight map "Corvette" for this, as it is the smallest map.
Set the difficulty to Normal or higher, doesn't matter since you cannot be killed.
As for the gametype, you may find it in my File Share.
You should get both achievements within ~30 minutes.
EDIT: TA user KHarttt mentioned that using the unlimited Jetpack can get you the achievement for killing 10 enemies while using the jetpack (Game Breaker achievement).
EDIT 2: TA user KAW 24 mentioned that the solution could use a small guide on how to download the gametype.
Press X > Select Your Gamertag > Press A > Select Find Player