In case you like visual cues, here is a video of me playing through Vidmaster Challenge A.
A few tips:
- I bought the Shield-Booster, but it's not a necessity
- the battle rifle is quite effective on all types of enemies in this level
- make use of your grenades
- take it slow, keep moving and keep your distance
- exploit the first turret to deal with all enemies surrounding you
- while driving your warthog, focus on getting from A to B and not too much on combat