This is pretty easy actually. There are both Quint and Jaws missions. One way to easily start a Quint mission is to hit either of the orbits 4 times.
To start a Jaws mission just light the 4 letters of Jaws on the in and out lanes then hit the lower left sinkhole. You can do this between balls too. I had 3 orbits plus all Jaws letters lit, then lost the ball, Hit the last orbit, then hit the sinkhole and got this. First try on this table.
There are other ways to start a quint mission, this was just easiest for me.