While playing on either table, after completing both the events mentioned elsewhere (catch Groundon/Kyogre and Rayquaza, on the same ball/turn), the Apparition stage will appear on the slots. Alternately, catch three Pokemon, although the slots are easier. Once the Apparition event is activated, hit Jirachi three times (who appears on the table, unlike the other Bosses which teleport you to a different stage) and you will catch it.