Show me, don't tell me.

Focus on showing how you excel at solving your customers' problems or pain points. Do this by:
-Blogging on relevant topics
-Commenting on forums where your target customers are engaging in discussions
-Publishing videos wherein you discuss a particular issue your audience struggles with
-Doing public speaking where your target market may attend (e.g., MeetUps)

Let the establishment of your expertise be passive. Your audience will decide whether you are an expert regardless of letters after your name.

Life coaching isn't on par with being a psychologist so credentials don't matter in the same way.