Some people couldn't receive this achievement even though they passed 18 gates. I managed to receive it. Here I explain what did I do to get it.
Adventure Achievement Guide
A Couple of Disclaimers
This guide does not include any other achievements. Meaning, in order to get other achievements, for example, "Transcendence" (find all the glowing symbols/glyphs in one or several walkthroughs), you will need to play this chapter again, with different paths and actions.
This guide will only explain a specific moment in getting this achievement. Meaning, in order to get the achievement, you need to make sure you have been passing all the gates possible before this moment. But there's not much to explain in that, just stick to the left and try your best to pass them.
Some people have been facing a problem. They couldn't receive the "Adventure" achievement (pass 15 gates in the sunken city), even though they counted the gates they passed and made sure to pass enough of them. Some of them even had 18 but still didn't get it. I've been having this problem too. But this time I decided to take a slightly different route and I got it. Perhaps only some specific gates can trigger it? I'm not sure.
I attached some screenshots below to help you see and understand what I mean visually.
How to Solved It
Anyway, the way I got it was: after the "pause" (where you stop surfing for a bit and can also release 4 groups of cloth creatures) there were three gates before the tower ahead. I decided to pass 2/3 and then held the "D" button to go as far to the right as possible because I saw there were some more gates and didn't want to skip any. You can also try holding "D" ("right") and "S" ("back") buttons while also using your flight ability (if you have any) to slow yourself down so that you don't skip the first gate out of those on the right. Perhaps you can even try going through 1/3 gates that are in front of the tower? Who knows. After that, I just tried to hit every single gate I could. And... It worked. Even though I skipped one gate there (I think). I didn't count them, but it worked.
Also, I got the achievement instantly, at the moment when the gate area was finishing, so, as far as I see, there's no need to finish the chapter.