If your goal is to get the Steam achievement, I recommend playing in the easiest difficulty, since this will be sufficient to get it.

Turrets and buildings you will need to unlock before starting: Drone Station, Repair Station, Shield Ray Turret, Last Bastion, Railgun Turret, Nightbay, Turret Beacon, Whirlwind Watchtower (none of these are optional for this method to work)

In Drill Core, you can currently only go to a depth of 1000m, which means that after you reach this point you can no longer mine any additional resources. Mine all the iron and swarmlit on each level before moving down to ensure you have enough resources to build everything you need once you reach the bottom.

Don't worry too much about how you place buildings, you can always destroy and rebuild them later. On the walls, use Laser Turrets at the bottom with one Shield Ray placed as high as possible. The point of this is to stop the bugs while they are still in range of the middle section turrets. In the middle and top sections use Rail Guns and Slowing Lasers (see picture bellow).

For nighttime abilities, use Drones, the Turret Booster (boosts multiple turrets) and the Nightbay. This will effectlvely give you access to double the number of drones and allow you to boost up to 10 turrets at the same time, raising the effective number of turrets from 18 to as many as 28 while the booster is active.

As you pick up technologies, make sure to get all 4 Watchtower types in addition to the turrets and buildings already mentioned above.

In terms of daytime abilities and other buildings, it is up to you, but I would recommend using the Resonant Laser, Worker Booster and Daybay. A Recycler will also come in very useful, since you will have too little iron and way too much swarmlit in the late game. Be careful not get your workers killed too often so you don't waste iron on rebuilding them.

By day 40-50 you will reach the bottom of the mineshaft. After gathering the last resources, kill all your miners and carriers (with "F"), make sure to have 5 barracs, build the maximum number of guards and then destroy the barracs. Additionally, destroy all buildings related to daytime abilities.

Build 5 of the following: Repair Station, Turret Beacon, Machine Gun Calalyzer, Laser Catalyzer, all 4 Watchtower types, Turret Booster, Drone Station and Nightbay. I would also recommend to have 4 Labs, and an empty spot where to build a Last Bastion.

Ensure that the watchtowers are as low as possible, so that bugs cannot move past them.

Now comes the boring part, make sure to use your abilities as freqently as possible and once it is day, hold "R" to start the next night. Your core should never be touched except by the boss creature. The Slowing Lasers together with the Whirlwind Watchtowers will keep the larger bugs stuck in the middle section preventing them from reaching the bottom, so you will never be in any danger, even as they get stronger, it will just take longer to kill them.

Around night 120 or so, a second Arachnor (the boss) will show up. This is the only critical moment where you are in any danger of losing the run. Make sure to build a Last Bastion to soak up the damage to your core and don't skip the day after the first half of the encounter, allowing the Repair Stations to work throughout the day.

Good luck!