Objective 1: Elimination
Objective 2: Capture Enemy Command Center
Recommended Echelon(s): AR/SMG (x2)

Note: This is doable with one echelon, but the enemies are quite easy, so it's not too hard to deploy two echelons for this map. Yes, even as a new player. It simplifies and speeds up the map by a good amount so that's why I'll be writing assuming you can deploy two. If you can't, take the time to clear around your base in early turns before moving forward to clear the objectives.

Objective 1 Strategy:#

So we've finally made to to where Sangvis moves now. This makes things much more dangerous since you have an additional fail condition in your Command Center being taken. However, being able to deploy two echelons makes this more or less irrelevant. 

With two echelons your main strategy will be to have one echelon start clearing the top of the map, then clear to the top left. You'll keep your other echelon on your Command Center to defend it, as well as to push towards the enemy Command Center later on if the Jaeger doesn't come over to you. Just be sure to take a Heliport to resupply, or resupply at your Command Center if needed. 

Objective 2 Strategy:#

Assuming you have a second echelon, you can let that defend your own Command Center while you rush to the enemy's Command Center. Just be sure to actually deploy it on turn 1. On turn 2 you can capture the Command Center.

Videos of me clearing this map

Objective 1:

Objective 2: