This is a Legacy of Rust achievement. The arachnoid enemies are fairly uncommon, and so an effective way to get this achievement is to repeat a part of the The Vulcan Abyss E1M06 : The Coiled City. I'm Too Young To Die difficulty is sufficient.
Progress through the first part of the level, descending down the first staircase, ending at the blood pool at the bottom. Pull the lever on the skull on the wall, then head out through the revealed exit to the right. Run across the lava, turning right heading toward the flaming wall, turning right again, where there will be the base of another staircase, with an incinerator and ammo sitting at the bottom. Grab it all, as well as some more health to the left side, then make a save point.
At the top of the staircase will be an arachnoid. Simply kill it with the incinerator, then load the save point. repeat this until you have killed the arachnoid 30 times.
Here is a video if you prefer to see it demonstrated :