I've been asked to give more details on determining a 'pirate' target for mission purposes. Ok here comes a brief guide with piccies

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The first step is obviously to fly your target system, in this case Patosata. Once there you need to try and determine your likely targets. Open up the Status tab in the right-hand panel and look at the various minor faction names:

In this case the pirate faction is fairly obvious as there is a faction called Raiders of Patosata. It's not always this easy, but generally speaking factions with names like gang or mafia are the ones to go for. If none sound particularly piratey then I'm afraid it's plain old trial and error until you find the right faction. Once you've determined your likely target head to a hunting ground, nav beacon or resource extraction site are best, for some fun.
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Once you've found a wanted target you need to check the faction in the contacts tab in the left-hand panel:

Proceed to kill the target, then check the mission in the transactions tab to see if you guessed right:

Generally speaking other ships of the same faction, within the instance, turn hostile. This allows you to identify other pirates quite easily.
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Once you've found the right target don't bother with anyone else, unless they have a juicy bounty or they declare themselves to be a pirate, usually they will scan you and ask for any cargo, there are a variety of lines that they'll use. These guys also count for the mission. Eventually you'll kill the required number:

You can see the effect you had on the pirates (and your rep) after turning in the mission:

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It should be possible to use similar methods to identify other targets. Smugglers for example will comment, when you start shooting them, something about stealthing there way this far and similar phrases.