The Festungsbahn is the short funicular that climbs the cliff face from the old town to the gate of the Kufstein Fortress, covering 56 metres of vertical ascent in under a minute. It operates year-round and runs frequently during daytime hours — there is no need to check a timetable. The ticket for the funicular is included in the entrance price to the fortress.
The approach at the base, where the old town square meets the cliff and the tracks disappear steeply upward, makes for a good photograph. If you are feeling energetic, you can also walk up the steep zigzag path on the far side of the cliff, which gives a different view of the fortress walls and the river below before rejoining the main entrance at the top.