There are '15' different badges - each has a bronze, silver and gold level, however you only need the bronze version of every badge for the achievement, you don't need to get gold.
These badges are quite easy and will most likely be achieved without thinking about them while completing the campaign, all except for 'Waste Management' and 'Hail to the Victor'. The former requires you to convert 40 power-ups into boost, if you missed this during the tutorial you can do this by pressing
when you have a power-up and a low boost level, just do this 40 times during races and it'll unlock. The latter badge 'Hail to the Victor' requires you to win at least 2 online matches and it seems only death matches count, I used 'Last Man Standing'. Also since the multiplayer seems to be pretty much dead you could just boost by inviting another player into an online lobby.
You can view the full list of badges and their requirements from the 'Game Awards' section of the main menu and whether you have achieved them or not, but here they are anyway for reference:
Rocket Ranger: 5 kills with a missile
Stuntman: Perform 100 stunts (just flying through small spaces seems to count)
Fighter Ace: 5 kills with the cannon
Shocker: 5 kills with the Shockwave
Mechanic: Use repair 5 times
Dedicated Miner: 5 kills with mines
Unpenetrable: Use the shield to block 150 damage
Frequent Flyer: Fly in-game for at least 1 hour
Waste Management: Convert 40 power-ups into boost
Hovercraft: Fly close to the ground for 7500 meters
Duraluminable: Survive 100 damage in one plane
Afterburner: Boost continuously for 5 seconds
Serial Killer: Kill three opponents in a row
Booster Pack: Boost for a total of 1 minute
Hail to the Victor: Win 2 online (death) matches