Too bad they would play out as a powerpoint slide....
I've gotten past that part going both ways. If you want to go left, you snipe the turret from inside the building you enter from, hug the center wall that curves around, and dash across the left side leaping to try to throw off needles and such. Make sure to toss a grenade when approaching the jackal and grunt. It will just blow them aside and you can sprint past them into the area with the wild creatures.
Otherwise, you can ignore the turrent and go right instead, sprinting and leaping into the building which allows you to get across the area safely inside and then just hop out and hug the right side (do same grenade technique for grunt/jackal). This strategy works best by yourself but it's a little trickier with other people. What happens is that the fire and nades that miss the lead person will catch the others. You can do it but you have to make sure everyone runs together and approaches the building entrance at the same time rather than single file so everyone dodges the fire together.