Lack of compatibility unsolvable?

My Gf (28f) and me (30m) are dating for about a year now and we have come a long way as our personalities do not align pretty well. Currently we are at a breaking point as we have tried so many things talked a lot be were not unable to resolve our problems. As a bit of background: I grew up in Europe she grew up in South America with cultural background in Asia. I just recently moved she is in the country for over 15 years. Our differences did show in the beginning, but what was new and exciting got more and more challenging after the months. I am calm not very extrovert, she is quirky and very talkative. Her perfect weekend/holiday is lying in bed relaxing vs I always want to see new things and walk around as much as I can. I like to spend my holidays in a mountain area incl. hiking, she wants to go to a beach/spa and relax. When I think something is funny she things it’s weird and not funny. The same applies for me the other way around. She likes indie/rock music I like hiphop/rnb. I like cats she likes dogs. I like the countryside and calming nature she likes the buzzing sounds of a big city. These are some examples but there is more to tell. We for sure align as well on things like marriage, kids, some movies/shows, gaming/board games. We had several fights over the past months and we are less and less resolving them as no one has the answer. Fights are mainly coming from misunderstandings, lack of communication and the fact that we cannot understand certain reactions of the other one. Right now we are trying to keep some distance but the grieve on both our sides is high and we both just wish the other one back. But without making a huge change we know we would end up back in the cycle. Is there any couple that also was faced with fundamental differences in character but where able to work it out? Or is there just no hope for us to make it long term.. I would be happy for any advice!