Easy enough, though I did need a restart because of a ball toss. Easy herding, basic R behavior. Actually, the first thing I thought of when I first saw the title was not Trek (I've seen all of those episodes numerous times) but Def Leppard... they've got a song on their second album, "High 'n Dry", called "Mirror Mirror". In fact, I now have it running through my head, but I don't mind - I like that song. I'm with @Meko Guy on this one... only two balls needed, in the 'deep well'.
Took me a while to realise how to get the balls in the holes, ! I love the almost symmetry, ! I only needed 2 balls, but having read the comments I went back to try the other side too.
After I stopped trying to do everything the hard way (herding R underneath the columns, having B in position for ball rolling w R pushing the ball) and discovered the far back sliders were VERY useful, AND there was an open/easy way to direct R up to the walkways...we won w 2 balls and then w 3! Sleek design + smooth moves = fabulous