This is more a clarification than a solution, since I can imagine I am not the only one who was slightly confused by the description of this one.
The wording on this is a little strange. I assumed that it meant "breach 300 times successfully", when in fact it means successfully use applications 300 times.
If you go to the Extras menu, and then Stats, it'll be represented by the stat that is describing application usage, not the one that describes successful breaches.