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Arachne is an assassin. She can be purchased with favor or gems, or rented if you do not own the God Pack.

Arachne's second ability, Cocoon ( if you use standard controls), gives her increased attack speed for her next 3 basic attacks. If you land the 3 attacks on a god, they will be stunned. This achievement requires you do this on 3 different enemies in one match.

So just keep track of who you have/have not stunned and you should be good to go! Since you need at least 3 different enemies, the smallest game mode in which this is obtainable is 3v3 Joust.

Here are a few other notes:

There will be a visual effect of the enemy being wrapped in a cocoon and visibly stunned when this happens.
If you accidentally hit a different god with one of the 3 attacks, or a minion, or too much time passes, this will not apply. You must hit all 3 basic attacks on the same enemy right in a row.
If you're having trouble, slowing them with your spiders () should help you land your attacks.
You don't need to kill the enemy god, just stun them.

You need to use your 3rd spell or B, once the buff is activated for every 3rd attack (not spell) you successfully land on a god during the buff it will stun them for a short amount of time. Do this on 3 different enemies and the award/achievement should pop.