Ok I finally got it, you have to alternate between the two fixed machine guns preferably the one on the right of the construction site. If you lay it heavy on the belly of the helo it will force him down.
I cannot for the life of me figure out how to get through the Chapultepec castle gate. I'm there, the apache is there, but I can't figure it out.
Btw this is for GRAW 1 campaign mode.