The Achievement requires you to destroy 10 Vacuum Bots, they look like a vacuum cleaner and have a large light at the front. They are scattered around the DLC and hold items inside. If you prefer the Written/Text guide here you go:
>(You have to destroy all 5 Bots in Minerva`s Den BEFORE you get on the Elevator! Otherwise you have to start all over again, because you cannot get back up again)<
Minerva’s Den 1/5
Head to the ‘’Rapture Central Computing’’ area (North). Open the first two doors and there should be a Gatherer’s Garden. Head to your left, the Vacuum Bot is right there, on the floor.
Minerva’s Den 2/5
When you find the Hack Tool, go to McClendon Robotics. You will see indicators that show where the demonstration stage is. Follow these indicators and you should reach a big room with a bunch of enemies. The Vacuum Bot is behind a barrier on the stage.
Minerva’s Den 3/5
The third bot is also in McClendon Robotics. Head to your right as soon as you see the ‘’Robotics Workshops’’ indicator. Continue and enter into the room where there is the ‘’Workshops’’ indicator. Continue in this room, and you should see a door to your right. In this room, you should see a metal screen. The vacuum bot is in the hidden room behind the metal screen.
Minerva’s Den 4/5
When you get into the ‘’Air-Tite Archives’’ area, head to your right and you should see the ‘’New Accounts’’ indicator. The vacuum bot is in the next room at the end of the short hallway.
Minerva’s Den 5/5
You need the ‘’Gravity Well’’ plasmid for this one.
Head to ‘’Rapture Central Computing’’ area and follow the ‘’Corporate Offices’’ indicators. You should see a closed door with an electromagnetic locker. Throw the ‘’Gravity Well’’ plasmid into the space above the door to unlock it. Turn to your right, open the door in the right corner and you will find what you’re looking for.
At the very beginning, take the door to your right (Programming area) and use the ‘’Electro Bolt’’ plasmid on the switch (to your left). The bot is inside this little room.
This bot is also in the ‘’Programming area’’. (It's near the Spitfire game)
When you get into the room with four visible consoles, there will be a door to your right.
Pass through it, then pass through the second door, go up the stairs, take the door to your left, continue onto the small bridge and you should see the bot to your right.
When you pass through the underwater tunnel with ‘’Core Access’’ indicators, you should see a Gatherer’s Garden to your left. Take the stairs that are to your left. Turn right and the bot should be on your left.
Now, take the elevator behind you. When the doors reopen the next vacuum bot will be right in front of you!
You will reach a room with a flashing indicator showing Overdrive, and also people frozen into place. At this point, go up the stairs to your right, pass through the door and in this room, you will find the final bot.
Good luck while searching.