There are different ways to do this as long as your elevation is higher than the monster in question, but the most consistent way is to use the insect glaive weapon. The first opportunity you should have against a large monster is the Great Jagras. With the insect glaive, use RT+A to pole vault in the air toward your target's back and attack, which provided your stamina isn't completely gone should allow you to mount the monster. From here you can repeatedly tap Y to slightly damage the monster, and hold RT to brace when it tries to buck you off or A to repel back toward it with your grappling hook if it does manage to throw you.