I have not taken JLPT but I am taking some British exams in Japanese; I did not take GCSE (equivelant N5-4) because I surpassed it's level before I even had the chance to sign up and am taking AS-Level this summer (roughly N3). So I can give you some advice on learning. I am in my second year of studying properly.
Just need lay out some knowledge you may know, but I must make sure before I waffle on. There are three sets of characters used in Japanese - hiragana, katakana and kanji. The first two are syllabaries that are based on the three simple base sounds of a, i, u, e, o, whith a consenant attached. Hiragana is used for Japanese words, and Katakana for loaned foreign words, sound effects and emphasis (like italics). Kanji are Chinese picture characters. The basic ones can be very pictoral but the more complex ones are made up of these pictures and gain meaning from their parts. e.g. 日 means sun, 月 means moon (it is more curved like a cresent moon), and moon and sun together 明 means bright. Kanji have two sets of sounds associated with them each - multiple kun-yomi, Japanese reading, and on-yomi, chinese readings. There are roughly 2000 kanji that are taught in school that you need to know to read as an adult.
And now the technical language learning jargon, some of which you've probably heard too, I know. SRS stands for spaced repetition system. Many memory experts say that reviewing flashcards and such in increasing intervals just before you forget them can really help you remember words for a very long time. SRS systems are simply digital flashcard systems that tell you when to review certain cards to gain this effect. There are two main ones on the market - Memrise and Anki. Memrise is online and gamified by having a theme of growing plants by reviewing flashcards. Anki is offline and more bare but can be greatly customised to do a lot of helpful stuff. They both have mobile apps. I use anki. Mnemonics are stories you create to help you remember certain facts and are proven to improve your learning by activating your creative memory. You can have fun with them too. There are several courses for learning Kanji that use mnemonics, the most popular being Heisig's Remembering the kanji, often refered to as RTK. There are also many premade SRS flashcard decks for this course. I use Kondansha Kanji Learner's course which is similar. They both teach the meanings but only Kodansha teaches readings. However, the readings are best learnt as part of words because they change irrationally and cannot be predicted well. The Core 2k, 6k and 10k are frequency lists of the 2000, 6000 and 1000 (building on each other) most common Japanese words in newspapers, and they have many premade SRS flashcard decks. The 10k is generally considered to have a lot of useless vocabulary though.
Okay, let's get down to business. I'll start with what I've done, then what my mistakes are, and what my advice for your course of action is.
Similarly to you, I picked some things up in anime and eventually decided I wanted to really learn. I learnt hiragana and katakana using these videos http://www.japanesepod101.com/category/videos-s2/
and practised it hardcore by reading Naruto 1 in Japanese. For a while I stumbled around using Tae Kim's Guide to Japanese Grammar http://www.guidetojapanese.org/learn/grammar which is an amazing free resource that concisely goes over Japanese grammar. I practiced what I learnt on Lang-8, a site where natives correct your writing in return for you correcting their English (they're super speedy too) http://lang-8.com/. I also began watching dramas without English subtitles (which actually override some of your Japanese memory with the more familiar stronger English memory) sometimes with Japanese subtitles, trying to note down words where I felt like it and looking them up, but never stressing about understanding all the dialogue - as long as I was catching some words and understanding the story, I was happy.
At some point I found the hugely popular but very rough and near impossible to understand Japanese learning blog, All Japanese All the Time (AJATT) http://www.alljapaneseallthetime.com/blog/. It basically says, you need to learn all 2000 kanji using RTK, then study 10,000 sentences (not words, because single words often have many different meanings depending on context) using an SRS system, while spending as much time as you possibly can all day, every day listening to Japanese. So I started watching my dramas more often, I discovered Scandal and filled my ipod with them and discovered other bands along the way, got loads of podcasts and set about listening to Japanese whenever I was cleaning, eating, travelling, dressing, surfing the internet etc. Any time possible. It really got my ear tuned right in and Japanese became normal to me, even though my understanding still appeared to be low. Little did I know, I was making huge progress in terms of the world of tests. Having started learning in September, I took a GCSE listening practice paper in April and got 90%. Having listened to so much Japanese, the speech in the test recordings sounded so slow and contrived that it was a breeze.
However, I wasn't really sure how to find 10,000 sentences, so I ignored that and bought a textbook. Many people reccomend Genki 1 and 2, but they are both £50 and don't even come with answers in the back?!!!! So I did some research and found this older book that covers all the same material in one cheap volume with answers, the only problem is the audio tape is out of print but someone has it all on youtube - Japanese for Everyone (JFE) http://www.amazon.com/Japanese-Everyone-Functional-Approach-Communication/dp/4889962344/ref=sr_1_1?s=books&ie=UTF8&qid=1429391086&sr=1-1&keywords=japanese+for+everyone I tried to work through the textbook doing the excercises but it took so much tiiiiiime. So mostly, I just focused on Kanji, writing them out a few times, coming up with mnemonics (the books guide you on this) and reviewing them in SRS (have the keyword for the meaning of the Kanji on the front, try to write it, then look at the kanji on the back of the card). I got through 780 kanji in 2 months, but then I went back to school after an extra long summer holiday and stopped. Over that 2 months I experimented with using the core 10k deck as my 10,000 sentences. At first I liked it, but the fact that they were just words taken from newspapers and were so irrelevant to me, annoyed me and I did less than the 2k before quitting.
When I started back to school I took a GCSE reading practice test, got 1 question wrong (and it was marked by a Japanese person not me this time) and so signed up for AS-Level. I have a teacher now but they are very laid back once a week lessons where she mostly corrects my Japanese diary and talks at me about her life while I'm too scared to say much, so I really don't see lessons as necessary. I found a more structured advice website with a similar message to the blog previously mentioned, but with real helpful guides about how to do stuff called Japanese Level Up (JALUP) http://japaneselevelup.com/ I
realised that the best way to interact with my textbook was to sit and make an effort to understand the grammar points, maybe take some notes and then instead of doing excercises, which takes up so much time just for the sake of improving writing (it really won't help speaking), I just use them as part of my 10,000 sentences and learn them through SRS. And that if I reveiw words from dramas I watch, I remember them much better and enjoy it much more than by learning from some random frequency list made from newspapers of all things. I also jot down words from Scandal interviews btw. Anyway, I have made more efforts to make my immersion in Japanese listening more effective, by actively watching videos, learning words from them, and then ripping the audio from the videos onto may ipod, making the whole process more connected. I cut out all English from my ipod, and can now listen to it on shuffle getting a mix of motivating music and the more educational speech portions. And... I'll be taking the exam in May. I am (almost) completely confident. Oh and somewhere in there I started shadowing (repeating what someone says in a recording after them, copying their voice and tone) to improve my pronunciation to great effect - make sure you listen to the content a few times first or it's pretty hard. AJATT reccomends shadowing a lot of people, but choosing a pretend parent of the same gender to copy the most for consistency; I managed a pretty good Mami impression this way, but with the mix of shadowing other people, the way Japanese comes out for me isn't naturally a comical Mami impression.
What would I change? Mainly, I wish I had kept going with Kanji because not knowing all 2000 makes my reading suck. But I wouldn't recommend doing all of them before learning any grammar or vocab like AJATT says; do some in advance and the rest in tandem or you'll get bored. I would also have not left my textbook behind, I wish I'd finished it quickly. But I guess I had to work out what I was supposed to do with SRS first.
So my advice as a plan of action?
1. Learn Hiragana and Katakana, with those videos, and the many apps on the market
2. Learn 500 kanji using RTK
3. Go through a textbook (the free Tae Kim's Guide is fine actually, I just felt I wasn't being serious if I didn't buy a textbook) while completing the other 1500 kanji. Review the sentences in the textbook using an SRS system. If you use Anki, Genki and JFE have premade decks onlin, look here https://ankiweb.net/shared/decks/
4.When you're maybe halfway through your textbook, start trying to listen to a lot of Japanese and shadowing.
5. Once you've finished you textbook, make an effort to learn from the things your listening to.
6. Try to start reading easy manga like Yotsubato! and Doraemon
7. Get some JLPT textbooks and learn what you need for the test. You'll probably know a lot of it already
(That was really long.... some of the links haven't come up properly, but I really can't go back through all of that so, I'm sure you can manage. Hope I help a little).