There are 15 multiplayer missions to get through. They are as follows:
1.) The Junks Are Back in Town!
2.) Billy the Bin
3.) Four to the Lava
4.) Serial Lava
5.) In a Wormy Submarine
6.) Give me Five!
7.) V for Vendetta
8.) Space Wormity
9.) Saint Pete's Apostles
10.) Space Dividers
11.) Food Intoxication
12.) Gastric Issues
13.) Spikes Peak
14.) Chips Chop Back!
15.) Bump a Dump a Diddle Doo
You have to get the highest score out of everyone playing in your lobby on each level to attain this achievement. The best way to get points is to collect atoms:
*Blue Atom: 20 points
*Red Atom: 1000 points
The red atoms are rare but if you get them you will boost your score drastically. If you concentrate on collecting atoms rather than trying to get the most kills you should be fine. I did this in co-op with one other player and we helped each other through each of the 15 levels twice so that each could win. The person losing can kill a lot of the enemies while the winner stays in front and collects the majority of the atoms. Killing enemies does help but not as much as atoms do. Some levels are difficult to even get enough atoms so it might be best on those levels to let the winner get the majority of kills on those levels.
If you're having trouble getting through certain sections if this is your first time playing the game, remember that certain enemies can only be killed in certain ways and it may be difficult to find out how to progress at times:
a.) Some enemies can be stunned or suppressed with your whip, allowing you to jump over and get by them.
b.) The plasma guns (look like machinegun pick-ups but they have red energy swirling around them) are very useful and can kill certain enemies that you normally cannot kill with your machinegun.
c.) Certain parts of the level require you to look for a hook to use your whip to get through the area. They may be difficult to spot at times.
d.) There are certain spots where you simple have to push the controls to the left or right to go up or down to get past a slope, where normally you would think you be able to jump over.
e.) Using teamwork to step on or whip switches helps!
This achievement should be a cakewalk if you have someone willing to help you, or you can simply go against each other and keep track of who won each level, which is why I thought a list of the levels might be handy! :P