There are three separate systems for earning Specials: achieving certain score thresholds, collecting team flags and earning RBIs.
RBIs are collected at the bullseye targets. On ball 1, a target scores 1 RBI. On ball 2, 2. On ball 3, 3. On ball 4, 4. On ball 5, 5.
Collect Team Flags from lit rollovers and slingshots. Collecting all flags of a league (red or yellow) lights one gobble hole for Special.
Nudge, but remember that tilt ends game.