"어떻게든": "Anyhow", "Somehow", "By any means".
"-거든": "If", "When". ~It is not really used that often. It's kind of a literary style ending.
e.g.) If you meet him, tell him to call me. : 그를 만나거든 나한테 전화 하라고 해.
You may leave when you have done with cleaning. : 청소를 다 하거든 가라.
~It's also used when you want to tell someone something. So, it's just another way of describing and explaining. I think it's more commonly used than the first case.
e.g.) We can't give you a discount. Our prices are fixed. : 할인을 해드릴 수 없습니다. 정찰제거든요(정찰제입니다).
It might be hard to cook for me. I'm a vegetarian. : 나한테 요리해 주기가 까다로울 지도 몰라. 나는 채식주의자거든(채식주의자야).
I couldn't participate because I didn't get the notice either. : 나도 그 공지를 못 받아서 참가 못했거든(못했어).