LEGO The Incredibles

The ambient crimes are mainly criminals robbing civilians, which you can hit and return the dollar to the civilian. I would recommend either using a fast character (Dash), a flying character (Syndrome), or a freezing character (Frozone). Though it is totally possible to do it with any character. Since there isn't really a spot to grind it, I wouldn't make it a main focus. Just travelling around the city you will see them. If you beat the game and don't have all 50 you should just run/fly around the streets to spawn the robbers until you get the achievement.

Ambient crimes happen all around the city and will show up on your map with small red dots. There are 9 different challenges that you can combine in order to get the 50. If you hit pause, go down to Open Map, then use the to Challenges, then twice to see the challenges that will count for this achievement.

Breaking Baddies: There will be a group of 3 "bank robbers" hanging out. Just beat them all up.

Caught in the Act: There will be a person either jumping up and down or crying. Somewhere near them, a baddy will be waving around a money. Chase them until you are close enough and hit B to handcuff them. Then take the money back to the person to finish the challenge.

Fire Fighter: There will be a fire that needs to be put out. Use someone like FroZone to put out the fires.

Everyone's Hero: There will be a person stuck under a car, usually it looks like there was some kind of wreck. Use someone like ElastiGirl to pull the car off of the person to finish the challenge.

ScreenSlaver Denied: Tucked back into corners and under overhangs will be a setup with multiple screens that all have the ScreenSlaver logo on them. Destroy it.

Clean Up Crew: In random places, usually not out in the open, will be pieces of Omnidroid Wreckage. Destroy them. You will know it is something to destroy because it will flash with a whitish color.

Super Supporter: There will be signs with a picture of a no symbol over a super figure. Simply destroy the sign.

Part Time Mechanic: There will be a broken DevTech broadcast relays usually on a rooftop or somewhere up high. Use someone like Buddy Pine to fix them.

Each of these need to have 10 challenges finished to complete them. In order to get the achievement you need to have a combination that adds up to 50. I had 10 breaking baddies and caught in the act, 9 fire fighter, 8 Everyone's Hero, 5 of Screenslaver denied and Clean up Crew, 2 Super supporter, and 3 Part Time Mechanic. This adds up to 52 but I believe I did a couple and then quit the game. I'm not 100% certain but I believe that the 50 need to be done in one session. Also, you can do the challenges more than 10 times. For example, I did the caught in the act WAY more than 10 times but it didn't count more than 10 towards the achievement. I just ran all over the map looking for any of these. Keep an eye on your mini-map for red dots and listen for civilians to say help and look around for them.