You must open up all pathways WITHOUT turning on the power. This means opening up every door/clear debris on the map, and blowing open three (3) different pathways using dynamite. There are a total of three power switches on the map (one in the spawn area (Docks), one on the boat (Bridge), and one on the mountain facility (Human Infusion)). Do NOT flip any of these switches while going for this achievement, there is no way to turn off the power once it’s been turned on.
There are a total of twenty-three (23) doors/debris you will be able to open by using points, fairly simple. You will be able to open three (3) of those doorways right from the spawn area, five doors on the Lighthouse, seven (7) doors on the boat itself, and four (4) in the mountain facility. There is another door/debris from the Lighthouse Cove area, and another one in the in the Cargo Area kind of under the boat going to the Secret Pathway. There is also another one at the blue cave area (Lighthouse Approach) to the Beach, and one going from the Beach to the boat (Gangway). You'll probably open most of these doors just by going around the map, super easy.
There are three (3) pathways that will need to be opened with dynamite. Those pathways are in front of the lighthouse (Lighthouse Cove), behind the boat (Sunken Path) or from the left side of spawn (Lagoon) (can be accessed from either side), and up on the mountain facility (Facility Entrance/Loading Platform) (can be accessed from either side). They will look like a barrier of wooden barrels and sandbags, with the sandbag in the middle with a red ‘X’ painted on it. Once you have you dynamite (see below how to get it), simply place the dynamite on the barrier, and step back. Yes, there will be explosive damage if you stand too close, so back up after placing it. You’ll have a few seconds before the dynamite detonates, opening the path.
To get dynamite, you will need to kill fire zombies by throwing snowballs at them (I recommend aiming for the head, as that’s usually a quick kill with a snowball). It’ll take a few seconds after killing them with a snowball; a glowing yellow piece will drop where the fire zombie died; pick up the piece. You’ll have to do this a total of three times. Once you have the three pieces the fire zombies dropped, you’ll be able to go to a buildable table, and construct your dynamite (don’t forget to pick it up once you build it). Three buildable areas; one in the lighthouse (Lighthouse Station), one on the boat (Gangway), and one on the mountain facility (Specimen Storage).
One dynamite blows up only one pathway, so you will have to repeat this step three times to acquire three dynamites total. I’d recommend as soon as your get your dynamite, blow up one of the barriers immediately. Fire zombies will not spawn in until you’ve used the dynamite. You cannot hold more then one dynamite at one time.
Once you buy your final door, clear the debris, and blow up your final barrier, (again, assuming you have not turned on any of the power switches) the achievement should pop.
Not my video, but one detailing the paths that need to be opened: