A lawyer, in order to work through a tight spot, must thoroughly investigate even the smallest details and check the same things over and over.
Literal
Lawyer [called-というもの] [topic-は], predicament [obj-を] break-through [in order to-ために], trivial points [about-についても] thoroughly investigate, same things [obj-を] repeatedly investigate-try [nominalizer-こと] [subject-が] important is.
A long, formal sentence packed with patterns. (1) ~というものは frames a generalization about a type: 'a lawyer (as a type of person) must...' (2) 切り抜ける (compound verb: 切る + 抜ける, 'cut and break through') = 'to get through, navigate (a difficulty).' (3) ~ためには ('in order to X') states the purpose. (4) ~についても ('even about X') with contrastive も. (5) 徹底して is the adverbial of 徹底する ('be thorough'). (6) 反覆 is a somewhat archaic writing of 反復 ('repetition, reiteration'). The final nominalized clause with ことが大切である is the aphoristic 'it is important that X' closer.