EDIT: Don't waste your time reading the solution just to downvote it. People are saying that most of the minigames mentioned here only appear nowadays in the Downtown map. I have no means to check that out since I've long completed the game and don't play it anymore. Anyways, I've came up with these ideas while playing it a lot and they worked for me. If they cannot be used for all maps any longer I hope that those who decide to read this solution will be inspired to seek and use their own creativity to find new ways to beat the challenges.
The first part of the job consists in getting the said percentage of Chaos from the sum of the minigames BEFORE the final battle (the Defend the Vats last stand doesn't add more Chaos to the count).
Here's the list of minigames I recommend picking and the ones I recommend avoiding when voting:
Wrecking balls - this is a good minigame to give everybody a chance to earn the bonus multipliers in the post game spin screen. Nobody is competing with nobody, except themselves. One bonus objective is to kill 20 enemies, the other to kill 40 of them.
Vending Vandalism - a nice game but one that requires excellent teamwork in order to complete it under 2 minutes. The first set of 9 machines spawn right where you are and everybody will probably take part in their destruction. As soon as the "Go to the next area" warning appears, instead of going towards it, if you're already used to this minigame and map, go to the third spot instead (it won't be marked on your screen so you need to know how to get there, which is easy, pretty much just follow the road hugging the invisible wall). Then, right after your teammates finish cleaning up the second one, the final 9 soda machines will appear and you can start destroying them, without awaiting for the rest of your squad. That's how you complete it efficiently in under 2 minutes.
Day of the OD - of all minigames, this is the one that I haven't played many times at all. So, no good tips here.
Fizzco Ambush - THE BEST mission in my opinion. Should be selected every time it appears in the voting screen. As soon as the game starts, pull out your Hair Spray Bomb (preferably equipped with the Second Amendment amp), jump forward and move down the road shooting everything until you don't see any red dots on your radar anymore. Keep bouncing on cars for extra points. Then start going back for that's where the next robot enemies will appear. Again, keep jumping on a car. When you get good on this mission, using the mentioned weapons, you'll get the most kills in it everytime. All in all, it's a short mission with lots of explosions and quick points.
Defend the Hospital - My tactic here is to stay away from your teammates from the beggining. As soon as the game starts, go South (check map) towards that big blueish building that looks like an underbridge. Stop between the numbers 4350 (on the right) and 4020 (on your back, on the left). From where you are, enemies will spawn in a few seconds, coming from 3 different doors. You can set up Acid Sprinklers and Turret Copters, besides shooting with your Hair Spray gun. Keep bouncing on the top of a car for extra points. It's guarantee that the biggest score and number of kills at the end of the round will be yours.
The Floor Is Lava - 1st golden hint: instead of rushing to the start point where everbody spawns, stay BY the Vat above the lava part (coming from the starting point of the mission, the first Vat to the right). That way when the mission starts, you'll be ahead of the others and really close to the first "pushie" doll. 2nd: after delivering the first doll, go back using the same upper way that you came from instead of jumping down and trying to slide through the lava like most people do. Keep doing that until you've collected as many as you can (I've collected all 6 a few times that way). Also, pay attention to your radar, it will show the locations of the dolls. Sometimes a couple of them spawn in a very safe area, away from the lava and close to the delivering point.
Scrambler... something - NEVER choose these "collect the numbers" kinda mission. They are one of the easiest to fail, no matter how hard or excellent one team member performs.
Fizzco HQ (a.k.a. "destroy the boxes") - In time I started hating this mission, for I was divided between finding and destroying 10 jedi robots for the bonus objective or focusing on destroying as many boxes as I could. Truth be told, it's hard to find more than 5 blue sword robots, left alone be able to kill them undisputed. Depending on the other option at the voting screen, I'd pass on this minigame.
Urban Jungle Gym IV - The least generous minigame to choose from. Only 1 player will get both bonuses for its objectives. After I grew a conscience, I stopped picking this game when I had a better option to vote.
If the tips mentioned on this solution help you in any way, please give it a thumbs up to let me know. Thanks!