Grammatically speaking, although we can use "when" in relative clauses describing time expressions, it's not the case in this particular sentence because it's an example of cleft sentences. The writer or the speaker of the sentence wants to emphasize "in that month" and thus places it after "It is/was". Then comes the relative clause about this time expression, but the clauses in cleft sentences are not fully governed by relative clause rules. Because of the preposition "in" before "that month", the clause should start with "that":
"... it was in that month that many of his greatest achievements occured."
"... it was that month when many of his greatest achievements occured."
PS According to Cambridge Advanced Grammar in Use, "when" and "where" can be used only in informal English. Thus, it'd be best if a native speaker could inform us about how natural and frequent they are in actual use.
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