Appistoki Peak is featured in Edwards’ “Routes Among The Peaks” on pages 315-316 in A CLIMBER'S GUIDE TO GLACIER NATIONAL PARK. If the completed Scenic Point Ridgewalk is taken Edwards states in his guidebook that the trip should take about 10 hours (it took a climbing partner and I about 7 hours to complete but we did not linger at any summits).
The route also crosses unnamed peaks and allows access for other peaks in the area such as accessing Mt. Ellsworth on an extended ridge walk.
If the desire is to do Appistoki Peak as part of the Scenic Point Ridge Walk continue up the trail when reaching the first switch back above Appistoki Falls (it is obvious as the great face of Henry can be seen from this switchback) and follow the route on the Mount Henry page. Avoid the temptation to attain the ridge above by climbing through the cliffs above the switchback. It takes much longer and traveling on the trail is easier.
For details reaching the Two Medicine Valley and the Scenic Point please refer to the Appistoki Peak Main Page.