He broke through the barrier of the university entrance exam.
この交渉が最大の難関だ。
This negotiation is the biggest hurdle.
He broke through the tough hurdle of the entrance exam.
After overcoming many difficulties, she finally cleared the hurdle.
He took on the difficult challenge of the bar exam.
I have an important hurdle coming up next month.
難関 refers to a difficult barrier or hurdle to overcome (like an exam), while 難局 refers to an ongoing difficult state of affairs.
難関 is a noun for a specific difficult hurdle or barrier (like an exam), while 難航 is a verbal noun describing an ongoing process getting bogged down.
overcoming a difficulty; breaking through a barrier; clearing a hurdle