"Subject-verb" is not a technical term in grammar or linguistics. It's a term some teacher used to mean whatever verb or auxiliary the subject is thought to agree with. So forget about that term, please.
The question as posed
Which verb defines the tense of a sentence?
has no answer, because it's improperly phrased. Sentences do not have a defined tense. Tense is a property of clauses, expressed by inflection of their verbs. Since every clause has a verb, and some have tenses, that splits clauses into tensed and untensed categories. Infinitives, gerunds, and participles are not inflected for tense, and therefore are untensed, or "non-finite" (this is where "infinitive" comes from).
Tensed clauses are called "finite" by comparison, and a "finite verb" is one that has a tense inflection of either present (am, is, are, goes, has, have, gets, wants, ...) or past (was, were, went, had, got, wanted, ...). Those are the only tenses in English, and there's one or the other in every finite English clause. No future tense, and no perfect tense (there's a Perfect construction). Present and past are it.
So in the sentence presented, there are four clauses (because there are four verbs: needs, to make, to achieve, and was aiming). To make and to achieve are infinitives and therefore untensed. Needs is present tense, and was aiming is past tense, Progressive construction.
As you can see, no verb defines the tense of a sentence, since sentences don't have tense unless they're simple clauses. But the inflected verb or auxiliary defines the tense of the clause, if there is one.