I did most of co op stuff with my wife since we have 2 Xboxes but she cant aim fast enough for this one. I was struggling to do it myself by using a dummy, because every time at least one Silo would survive a single rocket even on easy with boom/cowbell, and the tank gun has a tendency to hit at your feet unless you jump when firing.
To solve the issue, if you are struggling to solo this with a dummy here is what I did that got it the first time I tried it:
1. Clear all enemies and raise silos.
2. Damage the silos first with a plasma pistol. It takes about 20 or so shots to make the silo start spewing fire but not explode.
3. Park your dummy WAY far away. I put it on top of the high hill to the left from mission start (the really high grey rock one, not the one with trees). From here its so far away that even zoomed in with rockets the silos are relatively small.
4. Place your main on a rooftop between the two silos nearest to the gate you face at mission start.
5. Zoom in on dummy and fire one rocket at each silo.
6. Immediately pick up your main tag controller and shoot the nearest silo to you (should be the one on the left when on the rooftop between the two nearest the gate you face at mission start). You should be firing your rocket right as the first rocket from the dummy tag explodes, unless youre VERY fast swapping controllers.
7. Turn right and fire your 2nd rocket at the last silo.
Damaging all four with a plasma pistol just until the point where they partially explode/destabilize and start spewing fire ensured that all four would explode with one rocket, solving my issue where there was always one that wouldnt, for whatever reason.