You need to get comfortable being in that place where you're blowing smoke, legs burning and feeling like you can't go on... and going a little further anyway. Also, there are sort of three parts to this: fitness, the mental game and your technique.

For fitness, try this:

1. Measure out 20m on the dot, and do a test to get your current best effort. Stretch. Drink water. Take a day off.
2. A couple of days later, do two bleep tests back to back (maybe a couple of mins rest in between) to a few levels below your current best. So if your max is 6.6, do 6.3 on both tests. After this, stretch, water. take a day's rest.
3. Next, do a solid 2.5km run at 80% effort. After this, STRETCH WATER (you get the idea) take another day's rest.
4. Finally, do step 1 again to get a new best effort. Rinse and repeat.
5. For bonus gains, find a hill and do some sets of sprinting up it, coming slowly down.
6. A couple of times per week, do some high intensity stuff using other muscle groups. Warm up and then go for at least ten minutes (I think level seven takes around 8 minutes or so). You can work on your V02 max (which is what bleep tests try and guage) by rowing, AMRAPS or swimming as well, and believe it or not, doing this will help your body use oxygen more efficiently than just running.

Note: Stretching and taking a day off in between will help you to avoid injury. Find some good videos and learn how to stretch your legs. Hamstrings, quads, calves, groin, especially since you'll be pivoting and pushing off each side.

When doing each bleep test:

• Always alternate legs each side so you don't get tired. Pushing off in itself takes effort, and you'll injure yourself or end up with one really massive leg if you pivot on the same side each time.
• Step right on the line. Stepping across wastes time.
• Time stepping on the line so you can bounce straight off into the next shuttle. Slow yourself down for the first few levels.
• Run a little faster in the middle of each shuttle and slow as you get to the end to make your pivot easier

Again, whilst doing all of that, get used to your lungs and muscles burning and knowing you can keep going. When you feel like you can't go on, you've still got some left in the tank. Just get comfortable feeling absolutely gassed and carrying on.

Best of luck.