The Long Jump achievement requires you to jump 300 feet. This page explains how to do so.
How to Unlock the Long Jump Achievement
To unlock this achievement, you will need to have reached Test Chamber 11, where you gain the ability to create both blue portals and orange portals.
It is recommended to to turn on Portal Funneling in the options to make this achievement easier.
First make a portal on a wall and then another on the floor. Jump down through the floor portal (don't just walk; you have to jump), then after you fall out of the wall portal, shoot a floor portal and look down at it to make yourself continue to fall without landing.
Try to find a place with two walls close together, so that when you fall out of the wall portal, you will slide down against the opposite wall into the portal on the floor, allowing you to fall indefinitely. It can also be helpful to create the floor portal while facing the wall that has the wall portal. This will cause you to rotate each time you go through, which helps you go through the portals perpetually. Just be sure to jump into the floor portal instead of just falling into it.
Your jump distance will increase for as long as you keep falling without landing. After you think that you have jumped far enough, move so that you land on the ground instead of falling into the portal. If your jump was long enough, the achievement is automatically unlocked after you land on the ground. Otherwise, just try again and wait for a longer time before you come out of the jump.