I figured that I would go ahead and make a more in depth guide so people could understand a bit more about the game and what exactly to do and stuff. Just kinda help out a little more. It is long with a lot of information, but trust me, I wish I would have known some of these things before starting. I learned along the way, because the game does not really explain anything for you.
In order to get the Beat That! rank you must win 720 out of 780 flames at least. After you have 720, just back out to the difficulty menu and achievement will POP!
The game is split into three different difficulties: Turbo(easy), Nitro(medium), and Inferno(hard, and freaking frustrating). Each difficulty has 4 areas: the Bedroom, Mini Golf, Attic, and Bowling Alley. Then each area is split into three different types of races: Quick Race(which is the typical 3 lap race), Elimination(After every 30 seconds the person in last gets eliminated until only first place is left), and Rampage(by far the easiest, you have to destroy so many targets in a time limit, which is always more than enough time) and then after these three you go through 1 tournament which consists of 4 quick races you must win.
Now in each race you will recieve 3 flames for getting first, only 2 for coming in second, and only 1 for coming in third. Anything lower gets none. In tournament when you win it you get 3 flames. Also, you will have 2 bonus goals to achieve in each event(including the tournament as a whole) in which you get 1 flame for each one that you accomplish. In all, you can get 5 flames for each race. Most goals consist of: winning with a certain car, scoring so many points in the event(which is usually done just by playing through the event consisting of drafting:driving right behind someone, drifting: drifting around curves or in circles, and jumping: having really big air on jumps), drifting a certain total points(not difficult, but I would save those to come back and do later as it is hard to do this and win first place), getting so many direct hits, going through so many weapon rings(blue and yellow ones), landing a certain way after a jump(usually will get without trying), etc.. There are many different goals(most of them are very simple and you'll probably get them without trying). If you get the goal on the first try or not is not a huge deal. If you can, then try your darndest to get them and win first, it saves having to go back afterwards and getting 1 or 2 missed flames in each event or go back and win first, which I had to do and ended up with just the exact amount of flames to get the achievement. YOU WILL have to go back and pick up a few that you missed after winning all the tournaments, unless your just super amazing at the game.
I found the simplest method was make sure to get first in every race(towards the harder difficulties, you have to win first in all races to unlock the tournament anyway) and get as many goals as you can as you go along, but if you miss a goal you can always go back and get it, and as long as you already have the 3 flames for first on the event all you have to do is focus on the goal and it won't matter what place you end up in (except ELIMINATION, you have to stay in any position higher than last in order to stay in the event long enough to get the goal). Elimination is by far the hardest to go back and just get goals like drifting and such. My suggestion is, after you have won first in every race and gotten all the goals that were easy along the way that you could, then go back and get all the missed goals in Rampage first(you have plenty of time, and once you get the needed goals you just wait for the time to run out and its done), then Quick Races(just get the goals first then finish the race, doesn't matter what place you come in you still get the goal and it won't effect your first place goals), then Elimination (if you have too).
Now I went through and counted all the races I won first in: 154 races(if I didn't win first then I won second) out of 156 total races, got both goals in: 110 races, and only got one goal in: 34 races, and ended up with exactly 720 flames(so basically you need to win at least both goals in 110 races and 1 goal in 34 more races, or two goals in 127 out of 156 races or even to make it simpler just win 254 goal flames in all). Also as I said earlier, 1 type of goal is win with a certain car. This is a pain because they don't tell you the goal until after you pick your car(side note: they tell you both goals at the loading screen right before the race starts), so I went through and wrote down EVERY event you need to win with a certain car on and which one(Thank Me Later).
They are the same in all difficulties(Turbo, Nitro, and Inferno)...
Bedroom Area: Rampage event-Bedroom Brawl race- use Spectyte Racer.
Mini Golf Area: Eliminator event-Underwater Washout race- use Covelight Racer; Rampage event-Spooky Sprint race- use Mid Drift Racer; Rampage event-T Rex Rush race- use Bully Goat Racer.
Attic Area: Quick Race event- Hairpin Highway race- use Cool One Racer; Rampage event-Pinball Pursuit race- use Covelight Racer.
Bowling Alley Area: Rampage event-Bowling Ball Bash race- use Chicane Racer; Rampage event- Arcade Alley race- use Soo Fast Racer; Tournament event- use Jackhammer Racer.
There ya go, that should be everything you need, any more questions feel free to send me a message.