V těžké podmínky pracoval v Alpy.
The main verb is "pracoval" 3sg. past tense form of pracovat.
The subject is the nominative the implicit "on". Pracovat does not require a direct object, but is likely to take expressions that report a location; the preposition v plus Alpy is a good candidate for reporting a location. The preposition "v" in this meaning takes the locative case. Note that Alpy is feminine and declines like žena.
Těžké podmínky "difficult conditions" is preceded by preposition "v" that takes the locative case.