To me, the game doesn’t explain the parachute controls very well. And I think they’re all you need to win this achievement. So you just need one parachute in inventory; use a taxi to reach each of the 15 places; put yourself over the red arrow and press LB to play.
-Y button is used to jump off the building/motorbike and start the descent.
-If you still have the parachute closed, the left stick is used to move Luis during the fall (forward to accelerate), and shorten the distance between you and the landing spot/flying rings.
-A button is to open the parachute.
-With the parachute open, the left stick is used for precise rotation: left and right are used to rotate Luis, while if you press down (towards you, not the TV) the character pulls up his legs and you can go farther (that’s key!!!).
-LT & RT are used to fast steering, but if you use them at the same time (LT+RT) you slow the parachute for precise landing.
-The bottom-left corner map has a vertical line used as an altimeter. Use it as an hint to align yourself to the target (rotate and put it over the red dot). There’s also a black horizontal line that is your elevation, and a little red one that is the height of the next target, or landing spot.
As you may guess, the key is using rotation, L stick down and LT+RT, till you reach your destination. You don’t even need to touch the flying rings to win (they just gain you some money), just land into the bulls eye… or over the damn vehicle (aim at the front of it and slow down at the end!). That’s it! Good luck!