Build your monologue on tension, not character. Stories move forward based on conflict, tension and resolution, so find the central conflict of the speaker's character and design the monologue to explore that conflict.
Add variety of expression. Challenge the solo character to use his or her voice in surprising ways, from deep rich tones to lighthearted thin tones in the upper registers of the voice. (Indicate these in your stage directions.) The more variety in the character's expression, the less audience members will miss having other characters to broaden their experience.
Designate meaningful movement in your stage directions. A character wandering aimlessly does not maintain as much interest as a character who moves to various stage positions to create a sense of the places they are describing.
Give your character emotional range. Write contrasting scenes of sadness and elation and everything in between, so the monologue will provide a full emotional experience for the listener.
Include action. Even if your character only describes the action, the audience can imagine it, and this will provide contrast to the more introspective portions of your monologue.
Add character interaction. Your solo speaker can imagine someone else is present for a moment and speak to them. Remind your audience the character does not speak in a vacuum, and that other people are part of the character's experience.