Before diving into the specific strats and optimizations, it's important to get familiar with the most basic strats and functions of the engine of LIMBO. Knowing the how the physics work, especially momentum, helps you get a feeling for the boy's movement and not lose much time due to badly timed jumps or unnecessary walking.
The first and most important rule: Jumping is faster than walking! Well timed jumps are considerable faster than simply walking and probably saves minutes during a full run; however, simply staying on the jump button breaks the momentum of the movement. To get the most out of your jumps, walk two steps, perform a jump, land on the ground and as soon as the boy's second foot hits the ground, perform the next jump. If done correctly, you will perform another full jump without losing any of your gained momentum.
Reverse Momentum Edit
The reverse momentum is a simple move that abuses the possibilities of the LIMBO engine. By walking into one direction to gain the required momentum for a full jump, the moment you press the jump button, press the opposite direction. If done correctly, the boy will make a full jump into the opposite direction than the one you just walked. For a few scenes, this strat is extremely valuable, for example the boat.
In LIMBO, climbing over a ledge is an extremely time consuming move, so you want to minimize the necessary climbs in your run. Often it is faster to just climb up a ladder or a rope to the top and perform the jump on top of the ledge then, if that means you can skip the climb.
The boy's behaviour on slopes is a tricky one, as it can be both your friend and your enemy, since it may either speed up your momentum or break it. Try to never simply walk over the edge of a slope, since that will slow you down significantly, instead perform a jump to the middle of the slope to gain a lot of momentum and the ability to make a longer jump. This mechanic can be abused to get a boost at the very beginning of the game.
There is a way to climb over edges from ladders more quickly than otherwise and while it only saves a minor amount of time, this way of doing it is crucial to get Alien skip as well as optimized movement for the events that happen after Zetbox. To get the fast climb, before reaching the end of the ladder, on the controller simply press the direction the slope you want to climb on and A.