Each UFO has a number on it, and this is the number of times your must hit it to destroy it.
All UFOs must be destroyed.
Each beam has enough energy to travel along one line only.
You can choose the direction of the beam, but you cannot travel along the same line twice.
To fire, touch where you would like the beam to travel.
The UFO with the highest number looks the most formidable.
Focus your attacks on that one first.
Let's go over the first three steps.
First, hit the UFO with the highest number, then fire your beam at the top-right UFO and the uppermost UFO, in that order.
Continuing on from hint two...
From the uppermost UFO, send your beam to the bottom-left UFO, and then take the shortest path from there to the lowest UFO.
Finally, passing through the UFO with the highest number, destroy the upper-left UFO.
Then use your remaining energy to destroy the last UFO.
The answer is as follows.
top-right, top-left, top-right, bottom-right, bottom-left, bottom-right, left, top, top, bottom-left, right.