。
I must finish this work by the day after tomorrow.
Literal
Day-after-tomorrow [until-までに] this work [object-を] do-finish must-not [archaic-ぬ].
やってしまわねばならぬ is an archaic/literary form of the 'must' construction. ねば is the classical negative conditional (equivalent to modern ~なければ), and ぬ is the classical negative copula ending (equivalent to modern ない). Together ねばならぬ = 'must.' Feels stiffly formal or old-fashioned, rarely used in modern casual speech but common in written Japanese.