A gauntlet is basically a set of missions. in this case its 6 missions
you basically have to complete the first gaunlet which is normal difficulty and has 6 missions
all the levels are very easy and shouldnt give you any problems apart from mission 5 and 6
for mission 5 there will be 2 big enemies at the end you need to kill in order to proceed so make sure you save enough ammo for the last 2 enemies. if you run out of ammo just use your grenades or melee them.
for level 6 you need to clear 35/40 enemies in order to be able to finish the level