New research indicates that regular aerobic exercise can improve brain performance by its boosting of memory and cognitive processing speed.

a)performance by its boosting of
b)performance by boosting of
c)performance by boosting
d)performance, its boost of
e)performance, it boosts

The simplified phrase you want is “improve by boosting memory.” That’s a little obscured here by the “brain performance” put in the middle of the phrase, but still, that’s the phrase you want.