Human Fall Flat

Once inside the tower, you will find yourself in a room with a grid like floor with lava underneath and 4 vents in the middle of the room (1 not working)

Shoot yourself up to the platform above that has a door slightly open (with a yellow star symbol above) and then head through the door to now be outside the tower

Follow the pathway around to the left, jumping from platform to platform until you reach another locked door with rubble and a chair outside. Amongst this rubble etc are 2 batteries that we need. Start by grabbing one of them and placing it into the slot to the right of the door (as we look at the door)

This will open the doors, allowing us to put the other battery on the other side of the door (so inside the tower). Now grab a large piece of rubble from outside and place it so that when the doors close - the rubble blocks the doors from fully closing - i used one of the larger pieces

Now grab the first battery we used earlier from the slot and go through the doors that are still blocked by the rubble

I struggled initially to both carry the battery and get over the rubble but it popped once my body was fully on the other side

Go Fishing: 2:30
Time Saver: 3:30
Foot in the Door: 7:50

Tower Level #Xbox Achievement Walkthrough:

For those who prefer video guides here's my achievement walkthrough. I show this Achievement starting at 6:45 in the video.

When you're inside the tower, you need to move two batteries. After placing the first in the door, you can use the boulder debris to place where the door shuts, stopping the door from shutting after you've placed the battery to raise the lava. Take the first battery from the door, carry it over the raised lava, and put it in the other door. This should unlock the achievement for the shortcut.