As this game is open ended and primarily skill based, the only attempt at a walkthrough that can exist, without showing a stepfile or providing the music to a song, is one that contains suggestions at getting better and optimizing your ranking among the horde of other players.
First of all, you'll want to know how to regard each of the features and elements of the game present (gameplay options, difficulties, challenges, etc.). Check out the pages under Gameplay for additional info on those specific things.
You're going to want to begin with easy songs for a long time. If you've never played before, the first thing that you'll have to work on is hand-eye coordination, as this game is completely about reading the arrows for timing. The first thing most people do is play the game with one hand, as it's just easier to deal with your main hand (if you use both hands equally, maybe you'll find it just as easy to work with right off the bat). Either way, your play style won't really matter until you improve a lot. As people tend to get more experienced in playing FFR, their play style typically changes from one handed styles to more spread out two handed styles (such as the "A,S,K,L" setup). For now, it's really about learning how to play.
At a low difficulty (1-3 or so) you'll primarily be hitting individual arrows with large gaps between one another and the occurrence of a chord or paired arrow will be uncommon or rare.
- Two things to note
The more you play the better, but keep in mind that not all the stepfiles (the order that the arrows are organized) in the game match up to the music. Up to the first 20 or so songs you'll still be getting used to the game (especially because you probably haven't heard the songs you'll be playing to).
Later in the game you'll run across different stepfiles from different revisions of FFR. Older stepfiles remain static in color (all the arrows are blue), however some were revised in the past few years to accommodate for changes made to FFR (4th, 8th, 16th, 32nd, 48th, and 64th notes are color coded) (only older players would know of this change). Additionally, not all the arrows in the game reflect a beat or sound in the song. These rogue arrows are the product of an unrestricted stepfile system and can simply be regarded as an artistic liberty.
Also note that some stepfiles (mostly a few older ones) have horrible syncing with the music (such as Megaman 2: Dr. Wily theme or Revolutionary Etude); the only way to perfect them is to learn when to press the arrows, not how to press them in regards to the song (these songs are best played without sound, however decent scores can still be obtained regardless).
From the time that you start playing FFR to when you get to end-game gameplay (impossible songs), one thing is true: if you don't play on a regular basis, you will not get better competitively. Although you will probably see your skill improve significantly over time, it sort of tapers off like all skills do. At higher difficulties, not playing for a while will really deal a blow to your ability to read the arrows, how fast you can react, and how much endurance you have.
If you can download the songs from FFR, do so. Listening is half the practice anyways so if you know the tunes by heart you'll have no problem predicting what arrows will be appearing next.
One problem you might run into is memorization - if you memorize a passage incorrectly, you may mess up in the same place over and over again. You only have two choices to fix this: either play the song and concentrate until you can fix your habitual failure, or don't play the song until you forget it. The latter option isn't suggested as you may never really forget how it goes; plus you wouldn't be able to play that song, which is a bummer if it's your favorite song.
As you get more skilled in playing FFR, you must be aware of the option to increase your hyperspeed levels. If you start feeling as though you have reached a point where you aren't improving much more even though you are playing at least once every couple days, increase your hyperspeed by one notch, and you will quickly notice your skill increase. Just about all FFR players start off on 1x hyperspeed, which only can carry you so far. Once you start getting to difficulty 8 or 9 songs, you may want to consider raising your hyperspeed to 1.25x or 1.50x so you can get more view of the closely placed arrows. If you keep at it, hyperspeed can drastically help you improve your FFR playing abilities, as you will be able to send your body a much clearer message of what to hit when arrows come at you. You'll know when you are ready for hyperspeed...because after one or two songs from changing over, you will be astounded by how much better you can see and respond to streams and other patterns.
Becoming the best
Know the game - learn the terminology, understand the game mechanics, become a part of the community, get into the game. Do everything you can to immerse yourself: listen to the music, play the game, make your own stepfiles, etc. The more you can do the better you'll be.
Remember that the top players got there because they played daily, and they played competitively. You may want to turn on the failure settings (for instance, setting songs to fail if you don't get all perfects) to test yourself on different songs.
Your play style will have a significant impact on your ability to play the game, so experiment! Even if you only play one handed or two handed, switching styles will show you that you can play either way, albeit with a handicap on the single handed style.
You can also test your reaction speed, reading skills, and memory by increasing the difficulty of the gameplay with the aid of some of the settings available to you. These aren't necessary until you are attempting to perfect every song in the game.
If you are focused on creating a perfect account (one with a high score and low amount of played games) your best bet is to first create an account and play through FFR until you are extremely comfortable with the game and experienced enough to perform well on any song. Create a new account when you are ready and then pick which ranking style you want to perfect.
It's best to create a pure account that focuses on only one thing, as a multiplayer account will probably play just about any game (remember, low difficulty songs usually correlate to a tiny amount of points and you're trying to optimize your games played to total score ratio for a pure ranked single player account).
Remember to play only the most difficult songs that you have perfected, as these will give you the highest score without increasing your number of games played.
If you are going to create a pure ranked account, after you unlock everything on your normal account you'll want to send a challenge to your pure account with a ton of credits so you can play secret songs right away. This is based on preferences, and if you don't really like secret songs then don't worry about them. In the same way, you may want to unlock tokens for both accounts at the same time. Skill tokens should not be focused on, as some of them are quite difficult and wasting efforts on more difficult songs could potentially harm your rank.
Make sure to either score well or close the browser if you are failing in a song, as a failure is devastating to your overall statistics. Grinding through a "pure" single player rank is much easier than working on a multiplayer one, as it's hard to truly tell what the ability of your opponent is.
For multiplayer ranking, your best bet is to get to know your opponent before facing off against them. Spectate them, talk with them, and also check their stats available online (you can view how many games they have played and their total score). In this way you can see how well they do against other players and whether or not the account they are playing on has a lot of experience. Gauging the experience of someone based solely on their stats is difficult, however you should be able to match up another player with the stats you have just by comparing yours to theirs (a high number of plays with a lower total score usually indicates a truthful player that doesn't have an alternate account). Talking to a player is the most difficult way to judge them, as you can never be sure if they are faking something or not - it's probably best to disregard your conversations over skill with complete strangers.
The reason you are scoping out your opponent is so that you only face the ones that you think you will win against. A multiplayer rank is much more difficult to increase as you can only efficiently improve your rank by facing players with an equal or higher rank than you. However, high ranked players will probably not play players with significantly lower ranks because if they lose, they lose a large portion of their rank "experience." Your best option is to taunt a high ranked opponent into facing you, because even if you lose you won't lose much of your own rank.