Not sure what you are asking for - a correction or a translation?
1) Correction.
It is near perfect with almost nothing to correct.
"첫번쨰" is supposed to be written "첫 번쨰" (spacing), which is a negligibly small point.
I would also write "여행을 통해" instead of "이 여행을 통해", but that's just a style issue.
2) Translation
I have two dreams I would like to realize in my life. The first is to travel the world, especially Korea, Japan, Malaysia, and Turkey. By traveling the places, I would like to explore their diverse cultures directly.