: obstinately, strongly, firmly, decisively, strictly
"굳이" is used, when you insist "to do strongly and obstinately (by putting yourself at risk), even though you don't need to do or there is some risk that others can't agree with you or you will be criticized.
굳이 그렇게까지 할 필요는 없어.
You don't need to do obstinately?
굳이 혼자 가겠다면 그렇게 해
If you insist on going alone, please do so.