I have been pecking away at this myself. My tactic is just to do random BGs each day until I get a win (for the CP). Depending on which BG I get, I take a look at what achieves I need for it and keep those in mind so I can change my play based on what I need to do. For example, I need 1 more Tower Defense in AV for that achieve. So when I get AV, I tend to try to back cap after Galv.

Doing it at this pace makes it feel less like a grind to me because I'm never bashing my head for long.