It looks as if it wasn't pruned when planted and in its early years. I would start again and cut it down to about 12-15" in height and give it a good feed. You'll need to cut it regularly, and it'll be a few years before it gets properly established. Do an internet search to learn how to establish a privet hedge (I'm assuming that's what it is).

The good thing about privet is that it will regenerate after very severe cutting back. The common mistake with hedges is to be in too much of a hurry for them to get taller, whereas what you need to do is to stop the main growing point to encourage the plants to bush out near the base.

Couldn't you fill in the gaps with new plants that will merge in with the old, then you would still have the height?

Just realised - were you asking how to cut them back as you hedge trimmer isn't tough enough? I can only think of three alternatives: Buy a stronger hedge trimmer, use a saw or or ask a professional to do it for you. It isn't a very long hedge and should be relatively easy for them to do. And they will take the branches away for you as well...