As an update, I just went through the whole thing again, finally got the achievement, but how I got it... a bit weird.
Last week when I first tried to earn it, I was under the mistaken belief that everything had to be "flawless victories" like the description said, so I kept reloading after the 5v5 knight battle because, as I was playing on Death March, the allied knights went down almost instantly. So I set it to "Just the Story", and got the warning that "Achievements may be disabled if you lower the difficulty". I went on to beat the 5v5 with no losses, and the duel against the giant knight after, no achievement. So I thought the difficulty had something to do with it. (a quick google search tells me that, at least according to the Xbone and PS4 players, difficulty does NOT matter, "Just the Story" should be fine)
Today, I loaded a manual save I made before the whole thing, and stayed on Death March throughout. Beat every contest (though the 5v5 quickly turned into a 1v5), including the duel against the Rivian prince, no achievement. I thought, "Okay, maybe I need to finish the whole quest, since the tournament is just a means to help the cursed lady." Still nothing.
Then I thought... "what if I turn the game overlay on?" So I did, found the checkpoint from right before the 5v5 battle, and did that and the giant duel again, winning both. I waited during the cutscene, as Vivienne presented Geralt his golden sword. Finally, this damn achievement popped.
So... either the game overlay did it, or you have to watch the cutscene for the achievement to trigger properly (it popped after Geralt raised his sword to the cheering crowd). When I did the quest the first time, I made sure to never skip cutscenes the first time I watched them, so I'm not sure if it's the cutscene that did it. I'm hesitant to recommend turning the game overlay on because of all the problems it causes, but that's what worked for me.
It's worth a try, though.