Hi Daniel,
This up and down movement of the right stick with correct timing is essential.
Almost everyone that starts out doing this acceleration is very aggressive with it - I broke my first wooden stick doing this years ago.
If you get your timing right you shouldn't have to be too aggressive and your hand probably won't hurt as much. However this will come with practice.
Remember with the timing that as the diabolo is travelling down, you should be lifting your right hand. And as it's travelling up you should be pushing your right hand down. Make sure the diabolo travels above your head and down to around your knees.
Also I forgot to mention in the video that it's extremely important to keep the diabolo on the correct plane - make sure your stick-ends are aligned (this is exactly the same concept as doing basic lifting acceleration). If you find that the diabolo is wobbling and not horizontal, it means your hands aren't in the right position and the string is rubbing on the diabolo's cups (which slows down the speed of the diabolo a lot).
You can usually correct this through lots of practice

Also remember that new string is a LOT easier to practice this trick - old, rough and wet string makes it extremely difficult to learn.
Good luck!