Bonus Campaigns are rotating events that apply to certain games from week to week. If a game is currently part of the weekly Bonus Campaign playlist you will see a stack of coins icon in the upper left corner of the game title while scrolling through games:
CAPCOM description:
Playing Bonus Campaign games offers the chance to earn a lot of extra Caspo!
This achievement gave me troubles. The associated triumph showed as completed in the triumph list but I had not played a game with an active bonus campaign. Then after playing Progear while it had a bonus campaign, the achievement still would not unlock. I completed a full run through the game for the other bonus campaign triumph hoping that would work but the achievement still would not unlock. I then changed accounts from the title screen, then signed back in to my main acct, started a game of Progear, and the achievement popped.