Take a hat, take water, take your time. The views are simply spectacular. The ancient walls are as described, ancient, dont expect nice smooth steps and paths. Some may this and the steepness a challenge so just stop and breath in the scenery, it's not a race. Three hours should be ample time.
From the top Kotor and the Bay stretch out beneath and you can look look down on the little piazzas with their cold beers awaiting your return. Even if you only go half way it's worth it.
Dont do it in the heat of the day unless your fit and need the challenge.