HIIT will improve leg speed, however to improve endurance you need to do long slow distance runs.
Sounds like you are trying to join the Navy.
To meet the minimum requirement of getting to 6.1 on the beep test in my experience and advice to others trying to achieve this is to practice the beep test as much as you can in the lead up to the test.
Most of the problems are confidence. Make sure you have reached level 6.1 atleast once before you do the test so you know that you can actually do it. This provides much needed confidence on test day.
What you need to do is, as cliffy said, do some intervals. Level 6.1 is not that high, so I would advise for you do do 200 metre intervals. Aim to achieve 200 metres in 50 seconds, then have a 50 second rest. Do this 10 times. To change it up try doing 400 metre intervals. Aim for 2 minute 400m with a 2 minute rest, do this 6 times.
Do lots of beep tests. When you do a beep test go as far as you can, have a 5-10 minute rest then go again. When doing the beep test make sure that you aren't running in a continuous circle, make sure that when you get to each end you stop, turn and run back. You will be disqualified if you run in a continuous circle.
Try and do atleast 1 long slow distance a week. For your fitness level I would just be looking at around 2.4km (2.4km is the testing distance for RAAF, ARA and RAN when you get in so its a good distance to practice) Try to do 2.4km in 13-14minutes. Try to improve every week over the 4 weeks.
If you want any more info in regards to ADF fitness message me.
Hope this helps.