Lure the Kayran into attacking you with its tentacle, place a Yrden sign on the ground and then dive out of the way. When the tentacle strikes, it will get stuck. Move to the obvious weak point and slash the hell out of it with your silver sword.
Repeat the process three times, making sure to get out of the way while the Kayran flaps around after each tentacle cut.
After this you will be presented with a series of easy QTEs. Once done, a cutscene will trigger showing a bridge collapsing on the Kayran. Run up the ramp on the left to finish it off.
Note: make sure you loot the body from two seperate areas in order to get the Kayran Skin item needed for the Backbone achievement.