You will encounter many spiders through the course of the Autobot campaign. You will encounter them during the Kaon Prison Break, To The Core, and One Shall Stand missions. I got this during the To The Core mission but if you don't have it after that mission then do the following. During the final boss of the Autobot campaign he will start using an attack that summons spiders. He will start doing this when he is lying on the floor after his first 2 fights during the One Shall Stand mission. Just keep killing them at this point until you get it, which shouldn't take long.
You can also encounter these within the first few waves of Escalation if you are on the Autobot side, so you could just keep replaying the first few waves rather then re-fighting the end boss over and over
NOTE: Even if you die your kills towards the achievement will not reset, so you can be as careless as you want if you're just going for the achievement.