There are a lot of tall boulder problems out there. Problems on the Grandpa Peabody boulder at the Buttermilks, the problems at the Woodyard Arete in Yosemite, and other climbs in between all blur the line between bouldering and soloing.
John Sherman, the author of the second edition of Better Bouldering, put together a video with some useful tips on how to approach highballs.
Lyn Barraza, the manager at Berkeley Ironworks, climbed the highball Secrets of the Beehives at the Pollengrains. Lyn crushed through the bottom difficulties and then carefully climbed through the top sequence. Notice how she searches for the best possible sequence and isn’t afraid to return to a rest jug. Lyn climbed this problem ground up and employs tactics similar to onsight climbing on a route.
When Alex Honnold made his ascent of Ambrosia,he had toproped the top section a number of times. This allowed him to feel confident and move efficiently through the less difficult but scarier top sections. Inspecting the holds, breaking off loose rock, and chalking the rock helps a lot with confidence and moving well high off the ground.
Be careful when you’re high balling. The large the fall, the more likely you are to injure yourself. Have lots of pads and spotters. Be comfortable on the grade of the problem you are trying and stay relaxed up there. A calm mind climbs significantly better than a worried one.
Stay safe and have fun!