Hello, as i finally understand how to drive the chopper i wanted to share with you guys (PC only):

Take off: Shift (go to at least 100-150 feet)
Go forward: Use UP arrow + Shift + Space bar
once you see that the chopper start to go down release the Up arrow and Space bar, keep only the shift (you will be at cruising speed)
at this point you use only the arrow to go down (Up arrow) up (Down arrow)
Left and right are the same as usual
When you want to stop release the Shift and hit at least once the Down arrow and you should be able to use CTRL to go down or Shift to go up

I hope it could help you, for me its a game changer to pilot the chopper.