The game gives you random missions, three at at times. They are varieties of the following (credit to IGN for the list):
Brush Past Red Flashing Lights: Those lights appear near the top of the screen, and you might think they are part of the scenery initially. You will hear a sound when you fly next to them.
Collect Spin Tokens
Cover A Distance on Foot: This means you need to actually walk. Any distance covered in the air doesn't count.
Destroy A Vehicle
Finish A Game Between Specific Distances: Keep an eye on the distance you have covered, and aim for the closest zapper by the time you get close to the start of the target range. Keep in mind you will be sliding on the floor for several meters, so don't aim too far.
Have A Near Miss With Missiles: It's probably best to ignore that mission and let the near miss happen by themselves. Trying to fly too close to missiles or zappers just got me killed more often than not.
Have A Near Miss With Zappers
High Five Scientists: Remain on the ground and pass scientists. You will hear a clapping sound when you high five one of them.
Purchase And Use A Gadget
Reach A Distance Without Collecting Any Coins: Avoid using any vehicle or, obviously, the coin magnet.
Reach A Distance Without Using The Machine Gun Jetpack: Simply purchase another jetpack in the Stash when you can afford it. I recommend the Traditional Jetpack as you will need it for another achievement.
Rub Your Head Against the Roof: Fly to the top of the screen and remain there as much as possible.
Smash A Hole in the Wall: That hole in the wall happens when you start a new run. So you will complete this mission by playing a specific number of games.
Travel A Total Distance In A Vehicle
Some of them will be completed without even trying (gathering coins, for instance), while others will require a little planning (finishing a game between 200 and 400 meters). The achievement unlocks when you complete 10 of these missions.