One person is telling the following story to a friend of his :
I bumped into my old classmate John , the last time i saw him was 20 years ago , I said hello to him , but his response was so cold :
1) After he had gotten a PhD , he became so cocky .
2) After he had gotten a PhD , he has become so cocky .
3) After he got a PhD , he has become so cocky .
Which sentence is grammatically correct ?
Your first sentence is correct and fairly natural. You are talking about him becoming cocky in the past (simple past tense), and you are using the past perfect tense for "he had gotten" to emphasize that that past event happened before the other past event.
(Note that you could also just use the simple past there ("After he got a PhD, he became so cocky"), since you are using "after" already to explicitly order the events. In this case, both simple past or past perfect work interchangeably.)
However, it's important to note that in your second and third sentences, "has become" is actually not a past tense. It is the present perfect tense, which means that (even though it does say the "becoming" happened in the past) you are not actually talking about the past in these sentences. You are talking about the present state (he is cocky now (even though he wasn't at some point in the past)).
This means that in sentence (2), the use of the past perfect does not make sense, because there is technically no other past-tense verb for it to relate to there.
Sentence (3) does work (use of the simple past just says that he got his PhD in the past (which is true), and you're now talking about the present state of him being cocky), but as noted, this is talking about the present (him being cocky now), not any past event.
One other note about sentence (3), though, is that when talking about the present (instead of the past or future), it is more common/natural to use something like "since" instead of "after", so if you want to talk about the present state, the following would be more natural:
Since he got a PhD, he has become so cocky.
