You can do this without the swinging move, but your hero needs to have the wall-run and double-jump abilities.

When you enter the warrior shrine area, there is a small fence on the right. Go around it and position yourself by the mountain, as far to the right as you can.

Diagonal wall run to the hero's right. Although you cannot go that way, your hero will still ascend. At the top of the wall-run, double jump to the top, and you will reach the statue to unlock the warrior's shrine with no need to use the swinging bars.