The guide assumes you've played through the game once already and are familiar with the general areas and enemies of the game. Or that you are willing to look up what you aren't familiar with, elsewhere!

Start a new game at the easiest difficulty
Make a beeline for Molly and kill her to take her battery
Run through the little bandit camp and go to the Interchange entrance here in Slatten Dale. Make sure to go all the way up through to Central Processing.
Head out of the Interchange and to the church in Wyndham
Talk to the Vicar to witness the murder, then murder the Vicar and the lady there.
Grab the Vicar's key from the Vicar, then take the stairs up to the 2nd floor of the church.
Open the chest to grab another battery (2nd one).
Talk to Sims and report the murder, he'll give you free reign over the Prison Camp in Skethermoore to interrogate the Dr.
Go through the Interchange entrance here in Wyndham all the way through to Central Processing.
Go to the prison camp and grab the Signal Redirector from the Security room. You can ignore the Dr.
Go through the Interchange Entrance here in Skethermoore all the way through to Central Processing
Head back to Wyndham on foot, taking out two of the flame robots roaming the map for their batteries (that's 4 batteries total).
Head North out of Wyndham to go to the Woods.
Go through the Interchange Entrance here in the Woods all the way through to Central Processing (For the last time!)

Power up Central Processing with the free battery on the corpse, use your 4 batteries to power up the 4 data stores, use your Signal Redirector to bring up all the central consoles, then head straight for Oberon.

Once at Oberon, use the 4 explosives to destroy it, then haul ass outta there and to the bunker from the start of the game. You'll find the phone ringing around the area you woke up in, picking it up will get you the ending.

That's it! Generally you'll have to kill some soldiers here and there when you see stragglers for guns, so you can take out the robots, but they're pretty easy to kill. I recommend you do most of your killing in Skethermoore as that's where the soldiers tend to have "Stock" weapons as opposed to "Rusty".
Robots aren't too hard to kill, just focus down their fuel tanks and they should overheat allowing you to get behind them and yoink their batteries.
Folks in the comments can provide less hostile means of getting those last two batteries, check there!

Fun bug? At the time of writing, if you never pick up the phone except at the final moment in the bunker to leave, you'll get both the achievements for finishing under 5 hours AND never answering the phone.
Just happened to me, but I think it may get patched out.
In case you DID want to get that achievement while also doing this, I recommend you go with Joyce Tanner as a means of escape. She has the least amount of fighting to do, as you just have to get those radio towers up and running, and you should have a few hours to spare to do it. My run for the achievement took about an hour so, you should have plenty of time to pursue a different means of exit other than the operator.

Good luck!

Super short version
Kill Molly for battery 1
Kill Vicar in Church for battery 2
Report back to Sims to get free access to the prison camp in Skethermoore
Kill two robots in Skethermoore for batteries 3 and 4
In every area, make time to go through each Interchange door all the way through to Central Processing.
Once you have all 4 batteries, power up the 4 data stores.
Beeline to Oberon and blow it up.
Beeline back to the bunker you started the game in, answer the phone, gtfo. GG