Flying a Helicopter in GTA V?

What tricks do you have for flying a helicopter in GTA V so you don't look like you're tripping acid while flying? I really suck at it. I went to the flying school and I passed the speed flight and city route flying by 3 seconds each. When I'm flying I sway super hard left to right and can't seem to get it straightened out. The problem is mostly when I'm turning. I try to push the left stick forward so the nose of the helicopter points forward and turn only with R1 and L1, but when I'm trying to turn sharply I end up moving the nose of the helicopter when I'm turning and that causing the erratic flying. Also, any tips for slowing down so I can land more smoothly in a helicopter would also be appreciated.

I'm using Franklin, and have gone through all but 2 of the lessons in flight school so he's 100/100 in flight and I'm still experiencing the issues.