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This one was more complicated than I first thought and took me many tries to figure out. Once you have the idea though, it's not that bad.

The first thing to note here, is the poor wording on the achievement. It says you need to "resolve" a case despite the death of your team member. This is only partially true. You also need to catch the bad guys. If you send a lone cop, and he dies, then you send a second cop, the bad guys will have escaped and this will not count.

I was able to complete this both on steam, and iphone during the "Gang War" event. I had a motorcycle cop, with 2 cops in it, with no weapons or vests. I would send them to the call first and hope for the best. Before you send them in, have another cop or two nearby that has proper equipment and/or manpower. As soon as a cop goes down, whether injured or dead, send in your other cops. If both cops go down before you send them in, the bad guys will get away and you won't get the achievement. As long as the second cop unit arrives before the second one goes down, they can't get away. Hopefully one of those first two cops will die so you can get the achievement. If you're doing this on gang war, have ambulances at the ready as well. There will be lots of injured. Resolve the event and the achievement is yours.

The achievement (At least on the iphone) pops at the end of the duty. You will also get the purple heart achievement if you do not already have it.