One way or another, I have to wrap this job up within a month.

Literal

Somehow-or-other-[do-て] this work [obj-を] one-month [within-で] finish-[must-なくてはならない].

なんとかかんとか is an expressive reduplication of なんとか 'somehow,' giving 'by hook or by crook / one way or another.' ~なくてはならない is the classical 'must / have to' construction, literally 'it will not do if not (X).' 一月間 'one-month period' uses 間 'duration' as a suffix. The で here marks a temporal-boundary 'within / inside of' the month.