There are 3 ways you can activate a droid and obtain this achievement.
1- Make one from the Factory
To make a Droid you'll need the following skills: Industry, Craftsmanship, Manufacturing, Drilling, Smelting, Physics, and Engineering (You can also for Deposit in the Foraging side of the skill tree, but you'll more than likely have the Fire Biome already unlocked by then)
Here is a skill tree for those who want to plan it out themselves or to see what they need to be going for
https://forager.gamepedia.com/Skills The items you'll be needing to make the droid are:
2 Plastic (2 Royal Clothing, 2 Bottled Oil, and 40 coal)
2 Electronics (10 Crystal, 10 Obsidian, and 4 Royal Steel)
2 Fiberglass (4 Plastic and 10 Glass)
Once you have all of the needed items just go to one of your Factories and craft a droid, I'm not certain how long it takes but you can speed it up with Power Plants (up to 4) or hitting it with your Thunder/Storm Rod.
2- Purchase one from the Market
I'm not fully sure if the Supply skill is needed (3 skills above economy), but I would recommend having it as it gives you extra items sold at the Market. The items that show up at the market are random, but if you place multiple down you'll get a different set of items in each increasing you chance of getting one. From personal experience I would say you have a 1/60 chance of one popping up in your market and the price of one ranges from 9k to 15k.
3- Sacrifice one of your hearts of health at a Dark Shrine *not recommended if not a fan of save scumming*
A Dark Shrine can be found in the Fire Biome and the Skull Maze. Using one will give you two choices of a buff and the one you'll be looking for is called Terminator and will have a silver skull with red eyes as the picture. If you don't get that as a choice you can either pick one of the two options or just quit out of the game and give it another go, the choices are random so save scumming can help you get the choice you want without having to give up extra health.
I would personally do the Dark Shrine option as it is the easiest and getting your health back is actually pretty easy as you play the game and I never actually made my own as I got 5-10 from the market and the rest from the Dark Shrine.