I wasn't going to post a guide for this, but on my run I cleared the 4 minute time by a fair chunk so thought I would.
Video linked above, but below are text instructions for anyone that may struggle to keep up with the video:
- Spawn in, turn around and activate the Bathysphere lever until you die and respawn in the Vita Chamber. Note you can set the difficulty to hard here to die faster, then pause and switch back to easy.
- Leave the bathysphere, pick up the shotgun, electric buck, and first aid kits. Activate the door control to leave the room, then shoot the sparking door control to your left with electric buck and pass through the door.
- Pick up the eve hypos and first aid kits from the table on the left, then drop down to the level below using the gap in the railing found behind the splicer who is (attempting) to attack the lift panel.
- Head to the back right corner to pick up the trap bolt from the corpse, then head all the way to the left to another break in the railings. Pick up Static Discharge and drop down to the bottom floor.
- Pick up the electric buck by the Ferris Wheel lever, shoot the lever, and then activate it for Spin 1/6.
- Head left to find a splicer infront of some shops. Make him chase you back to the lever and allow him to hit you. Your static discharge will kill him and shock the lever. Activate the lever for Spin 2/6.
- Head right behind the wall to the carnival.
- Pick up Telekinesis, then use telekinesis to pick up any of the teddies to your left on the first carnival stand. Carry the teddy to your right behind the first carnival stand on this side, and hold the teddy over the fire. Once it catches fire, head into the back of this room and melt the ice above you. Grab the electric buck that gets freed up and falls here - if it drops through the pipe just use telekinesis to fish it back out.
- Head back into the carnival area and now head behind the stand with the teddies in to the room behind it. Activate the safe to trigger a set of trap bolts, then grab the nearest trap bolt with telekinesis and drag it to the safe to open it up. Pick up the crossbow then run through the trap bolts and out of the room (easy difficulty to avoid death is recommended!)
- Turn left in the carnival room now, we're heading for the back right room with the panel that requires a door code. Enter 1951 and open the door and get the splicers attention, making it follow you back to the main area with the Ferris Wheel lever.
- Allow the splicer to hit you by the lever and activate it for Spin 3/6.
- Once it's cooled down, shoot the lever with your electric buck and activate it for Spin 4/6.
- Turn around from the lever and head straight behind you into the toilets. In the back left side of the Gents is another splicer, get it to follow you back to the lever.
- Allow this splicer to hit you by the lever and activate it for Spin 5/6.
- Once it's cooled down, shoot a trap bolt at the lever and run into the bolt to activate it. Then activate the lever for Spin 6/6.
- Head over to the Ferris Wheel and watch as the Little Sister is freed. Once she climbs off of the Ferris Wheel and hops off the ledge to you, interact with her to end the level.