After passing the JLPT N3 exam with almost all the questions correct, and being in the top 3% globally, I signed up for the JLPT N2 exam, three months later.
In summary, three months is not nearly enough time to go from N3 level to N2 – there’s especially a big jump in the number of Japanese words / Kanji you need to know. Even the listening is a lot harder than N3.
The worst thing is that you only get informed of your results by mail, a couple of weeks after the closing date of entry. You need to know to check the results online before the two weeks during which entries for the next exam are open. As a result, it will be 9 months until I can take the N2 exam again. At least by then I should be ready 🙁
Update: I passed JLPT N2 in December 2021.