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 [plain-ない].
やってしまわねばならない uses ね(ば) + ならない (the plain modern 'must' construction). Still formal but less archaic than older 為さねばならない. The ~てしまう completion auxiliary remains.