Once you download the Raid update, you are then able to access Raids through the menu. To clear a gauntlet, you simply just have to finish all levels in that sector.
The first mode you will be able to do, will be Normal I, which is a pretty straight forward task. However you may have a bit of trouble with the last few levels, so I would strongly recommend collecting all treasure chests as you pass them. (To be honest, it is harder to miss them) Once you have collected them you then have to evaluate them in order to use them, which is also an achievement.
Just then equip all your 4 slots with weapons and use your ammo carefully. I would strongly recommend using a Rifle to take out the big guys with helmets on, just shoot in the red area below their head for the maximum damage.
That is pretty much all I have to say, as it really isn't that difficult. Last but not least, Good luck!