1) When you try to translate construction "something of somebody" always use somebody in genitive, case of something depends on a situation, in our situation it's subject, so we should use nominative:
The character of a people = Характер (nom.) людей (gen.).
2) Our predicate is "is tested", and it's in passive voice and describe present, so use the verb проверять (to test) in imperfective aspect (проверяет) with "ся" to make passive voice: проверяется.
3) The preposition в (in) usually is used with prepositional case:
в длительной оборонительной войне.
Result:
Характер людей проверяется (or испытывается) в длительной оборонительной войне.