Is there any benefit to completing the "Advanced" Augmented Reality Training?

Solution 1:

After getting the Grapnel Booster from the basic challenges, the only other reward you will receive is a trophy of the Batwing, which you can view through the menu.

There is, however, also an Xbox and Steam achievement for completing all the Augmented Reality training missions.

AR Knight

Complete all augmented reality training exercises

Solution 2:

You don't get anything else in regards to gameplay for completing the Advanced Augmented Reality Training. For completing them all, you get the AR Knight achievement. Unfortunately, completing all of the ART sequences is a Sidequest, so in order to get the Perfect Knight - Day 2 achievement, you'll have to complete them.