Not sure. In my opinion, the breach takes way too long to do for the rewards it gives. It should be at least doubled. I was very disappointed when I first completed it. I like the mission itself, its different, and navigating the ship makes it fairly enjoyable.
Spend a few hours on ground in the battlezone. Do the missions and get the one commendation mark and then take the other dyson marks when you get 350 and do the upgrade project to turn them into 5 commendation. You can probably get a weeks worth of stuff in a few hours of play on the ground. You will also get your days worth of dilithium.
Allied Space for Marks and Battlezone for Voth Implants. Can get 10 Marks every couple of minutes by just doing the Ion Sector mission.
That's the hard method. I'm currently sitting on over 2,200 Dyson marks on my Science officer with another several thousand spread across several other characters. Just grab a Ground PvP team and hit the ground Battlezone. You will make 1,000 Dyson Marks in an hour easily.
Do the Allied Space daily for the commendation and Battlezone for everything else.
Though honestly you could skip the Allied Space daily if you wanted to - you'll easily clear the 350 marks needed to get 5 commendations doing just Battlezone. I do the Allied Space one myself because I enjoy the space zone and because I'd prefer to use those excess marks to generate even more dilithium.