Don't specifically aim for this achievement as it will happen on its own easily as you play.
Just need to have someone get injured or killed on a call. Firemen can be injured fighting fires (Only if they do not have a fire suit) Police can be injured in any conflict, even with vests. (But less likely) Paramedics can be injured when there's something dangerous happening while they work on injured folks.
It may take several duties to occur, but it'll happen before you finish the campaign and/or while working on other achievements. I believe you need someone to be "Heavily Injured" for it to count.