。
Investigating it is a tedious, soul-draining job.
Literal
That [obj-を] investigate [nominalizer-のは] boring-[and-で] fed-up-do work [copula-だ].
のは nominalizes the infinitive clause 'to investigate it' as the topic of evaluation. 退屈で is the conjunctive form of 退屈 'boring' used as a na-adjective ('boring and...'), linking into the next descriptor. 飽き飽きする is a reduplicated compound meaning 'to get completely sick of / fed up' — doubling 飽きる 'to grow weary' for intensification. The two descriptors together stack tedium.