We'll stop at Kotor on a cruise April 2019. At a late-60-year-old pace (mobile but not an athlete), what is the duration of the walk from the bottom to the top, and from the top to the bottom? Also, is there some type shuttle to the top and then walk down?
Only "shuttle" would be finding some fool to carry you up and down. Good luck with that.
It's a lot of steps and walking on decent paths, but it is a long way up. An hour minimum if you move steadily and briskly and don't stop for many breaks. At a less aggressive pace, with reasonable breaks occasionally to catch your breath and allow your legs to stop throbbing a bit, I'd allow two hours up, one hour down. Hopefully your knees and other critical moving parts are not too fragile.
It is a lovely hike up (and down), the view is wonderful, but it's more physically demanding than I had expected. "Oh, walk the ramparts up the hillside behind town? Sure, sounds nice." By the time I got 1/3 of the way up, I was hoping there would be a nice bar at the top with cold beer. There wasn't. There was a guy selling small bottles of water for 3 Euros each that he had carried up in a backpack. I gladly paid for a couple.
My experience was a few years ago. With the explosion of travel there and all the cruise ships, maybe they've put in a chairlift and zip line (and that bar at the top)?
I climbed it last week and only went as far as the fortress. I went early in the morning before the heat of the day and crowds of people. It is a pretty steep hike up steps and uneven terrain and it is two way and the steps are narrow.
I took my time and it took me about an hour to get to the top, but I was also stopping for photos. I spent a good bit of time at the top. It took less time to come down, but by then, there were a lot more people.
There is no funicular, elevator or shuttle and sadly, no bar at the top.