This page explains how to find and climb Dueling Peaks Tower in Hyrule in Breath of the Wild.
Finding Dueling Peaks Tower
Dueling Peaks Tower is easy to see from the top of Great Plateau Tower when you look east, so use the Sheikah Scope to place a pin on Dueling Peaks Tower. The pin will be visible on your minimap, so you can just go toward the pin.
As you go east from Great Plateau Tower, if you go along the dirt road, you will go through the Outpost Ruins, then you will cross Proxim Bridge. Keep going east and you can follow the river to the tower. Once you get there, you can use Cryonis to walk over the water, or go across the rocks just west of the tower, or just swim at a narrow point in the river.
Climbing Dueling Peaks Tower
Dueling Peaks Tower has many platforms to rest on, so it is easy to climb. To save some time, you can go up the slope just north of the tower and float down from there. There is also an angled stone leaning on the east side of the tower that you can walk up so you don't have to climb as far.