Show your personality. Try to find something that reflects you as a person, something that suits you.
Be under 3 minutes. Two minutes is usually enough to show your stuff, so keep it short. In fact, auditioners often make their minds up within the first 30 seconds (a good reason to play with video Shorts on Soliliquio).
Have a clear objective. You can't just stand there and talk. You have to be actively talking to the someone you've imagined, and be trying to get something from them.
Have a beginning, middle and end. Beginning: a strong opening line to grab attention. Middle: lots of juicy content. End: a strong conclusion. An audience is more likely to remember you when your monologue is well structured.
We don’t always get to choose our lines, so practice making every scene your own.