At this point i assume you already finished the game's story mode (NFS Live series) and earned the easy badges mentioned above: US/EU/JP Manufacturer Loyalty, drafting, clean/dirty overtakes, trading paint... things like that you can do in Quick Race mode with AI or alone... Getting the 20 platinum badges is a bit harder work, but not impossible. Thank God you don't have to earn all of the badges, so you can deny the harder ones like beating all rivals, finishing first on every endurance races, master every EU, US, JP corners and things like that. Let's be honest: this game is not a good one, and it's very hard to obtain a good podium finish on a race, especially if you are not very good in racing games.
The Online badges are really easy, especially if you have a boosting buddy on your side. Winning on all tracks will give you 3 platinum badges: Online Europe, japan, US Champion. These must be done in a ranked game, but you can play it with only 2 players (counting yourself too of course). One win for each players on all tracks can be done within 3 hours. I suggest you to use the following race options: set the the race length to Short, (you cannot set a specify number of laps in ranked games), set the class restriction to unrestricted and use your fastest car. After a few races you'll have ton of money, but in case you don't i suggest you to use a loan car. For me the Maserati MC12 GT1 seemed a pretty solid, fast and driveable car. These races are also counting toward the 250 podium finish badge, which is the next badge i suggest you to work on. For that you need to achieve 1st, 2nd or 3rd place in online races - both ranked and unranked games are counting toward. Set up an unranked race with 1 lap on Miyatomi, (it's a very short oval track) invite your friend and rubberband the right trigger. In the lobby you can press X for voting a race start after 30 seconds, otherwise you have to wait 2 minutes until the race starts. For drifting badge it's nothing special.Just try not to obtain more points than your friend when he goes for the win. Vice versa. The dueling badge is a bit pain in the ass. For some reason it's not a lobby based gamemode, but a matchmaking system working under it. For me it didn't work. Not at all. I wasn't able to find my buddy while both of us were searching. So i just skipped this one.
Mastering the corners are a huge pain in the ass. Let's face it: this game sucks. It doesn't even able to decide whenever you mastered a corner or not. It doesn't matter if you had a speed in the corner and you followed the racing line. You must keep trying and trying until you have luck and you finally pull it in. For this reason i suggest you to only do the Japan Corner Master. There are only 6 Japanese tracks in the game with actual corners and they are surprisingly easy. These tracks have wide and short corners, with all assits turned on you can easily do them. I used the Nissan 240SX, it just worked fine for me.
Another easy one is the Perfect launch badge. You can start working on this while you are playing the Carreer mode. Basicly all you have to do to reach the right RPM at the start line. When the HUD switched green, you are good to go. On the top of the screen, where the XP meter is you can see a "Perfect start" subtitle whenever you did it right. It's also boostable: Fist thing is to turn off the autosaving. Then set up a private race on Miyatomi with 1 lap and no AI opponents. Use the car which is the most suitable for you. When the race ends, hit Y to restart the race. Repeat it until you got the 250 perfect starts. (Yes, before every restart the game tells you that all unsaved progress gonna be lost, but ignore the warning. Eventually, you will find the badge popping up after every 50 perfect start. Don't forget to save manually just in case if you have a power failure or something else comes up!!!)
I hope this solution will be helpful. I deleted my last one for the lots of downvotes and yeah, let's face it: it wasn't accurate and helpful. Good luck my friends!