is there any easy way to shoot the helicopters down rather than trying to shoot them out of the sky and die like 20 times...

I dont know why it takes you 20 times to shoot down a helicopter. but I found it easier to be a autorifle man. I shoot down at lest 7 or more before the helicopters with the rockets get me

My best suggestion is what i do and that is when the helos approach whip out your rocket launcher and let it get close to you then fire and one hit should kill them, or you can try to find a turret and hope to kill it

What I'm still trying to figure out is how to get my recon team to use their Zeus missile launchers. I used the one I had to take out the Blackhawk bringing in the mercs. I tried the "attack" command but all that does is make the team member concentrate on one heli.

The chopper bringing in the troops is not a threat, the soldiers are however, save your rockets for the two gunships, your guys have to have a clear unobstructed view of the gunship before they will fire, and yes it takes multiple times of ordering them to shoot before they do, I did it this way, have a gunship in the scope, then order whichever of my guys has the rockets to attack and keep doing it till he says understood.