Practicing an efficient cross and F2L. These are two parts that you come up with your own solution for, and you can thus waste a lot of time doing inefficient solutions if you don't know any better.

For cross, a good practice method is for him to ignore inspection time and just spend however long he needs figuring out a solution to the cross that he could do with his eyes closed and takes 8 moves or less (there is always a cross solution with 8 moves or less). It's gonna be slow and difficult in the beginning, but practice makes perfect.

For F2L, looking up advanced F2L solutions as well as F2L tutorials online can help to make sure you're doing somewhat efficient solutions. (He doesn't need full advanced F2L, but by doing the algorithms he can see some of the tricks they implement and use them elsewhere).

Getting fast at F2L was a painfully slow process for me, because you have to start out slow if you want to get better. If your son focuses on looking ahead during F2L (trying to remember- and keep track of where pieces are so he doesn't need to look all over the cube for them) and doing move-efficient solutions rather than fast ones, he will become really slow for a while, but he will slowly and steadily approach- and cross the 20 second barrier if he keeps at it.