Neither of your attempts is actually correct. What you want is:
- I need to get a high enough score to pass this exam.
- I need to get a score high enough to pass this exam.
Personally number 5. seems best to me since it doesn't separate the quantity from the goal. The "high enough" relates to two things. On the one hand to the score (the thing that needs to be high enough) and the other hand the goal (how high is high enough? whatever lets me pass me this exam). An even wordier version could also be
- I need to get a score, which is high enough to allow me to pass this exam.