Not sure how much time you have every day and if you can handle this immense work for 4 months straight, but I guess it’s possible?
I passed N2 (barely, mind you) in 1 year, working almost every day for 4+ hours, if not 8 sometimes. At the beginning I only had Genki 1 done, although I forgot a lot from it. After I did 1 Genki 2 chapter + all exercises from grammar book in 1 day, making notes and all that stuff. I moved to Tobira then, but quickly stopped after 5th chapter, and went for Bunpro for some time.
I was doing 2~ grammar points per day, so you can try doing that. Calculate the total amount of grammar points, divide by the days (4 months, so 120 days) and see. According to BP now you’d have to learn 3.5 grammar points per day.
Don’t also forget the vocab, that was a thing that killed me on jlpt. There’s a WK vs JLPT spreadsheet, add the words from level like 30 (or whichever you’re gonna reach on WK during those months with comfortable speed) and start adding them on SRS platform, don’t add the words you already have on WK, you can’t really spend your energy on that.
I used Kitsun’s 10k, it worked wonders for me. It has audio questions with your normal reading, meaning and English->Japanese, plus example sentences helped me a lot with understanding the word in context and listening. Do the same thing like with grammar, calculate the amount of words needed and divide them by days.
Don’t forget about listening too. I watched a lot of 日本語の森’s videos on youtube, like 3 a day from N3 and then N2, adding words/grammar to SRS when I see it. Recently I finished 国語 series, it was great for listening, highly recommend it after N3, closer to finishing N2 (link to the playlist).
I also read a lot, about 1-2+ hours per day for half a year, then I kinda stopped because I finished manga series and now I try to go back to it again. Look into bookclubs here on the forums. I started by reading Yotsuba with the help of list of words translated, which helped with understanding colloquial speech, and then I went full on with 時をかける少女, catching up to the bookclub, reading one week of work in one day, every day. That took so much effort and time, but it helped a lot with understanding long passages of text. I also read Breaking into Japanese, but oh boy was it challenging, but really fun.
All in all, it really depends on you and your ability to spend so much time and effort on it. Four months is really really hard for N2, but technically not impossible, that depends on your brain’s ability to handle this. Please don’t burn yourself out with this though, it’s not like it’s the best way to go about it. I lacked a lot of vocab and deeper undestanding of grammar points with that method, so you’d have to work on your weaknesses after this. Plus, it’s better to go steady for 1, 2 years than to stop after 1-2 months and be unable to go back to Japanese for a year or something like that.