Well, I’m only a new seller on Fiverr, but I guess I can give you some tips anyway.
First, you want to be THE VERY BEST in what you are offering: as Einstein said, “You just have to learn the rules. Then you have to play better than anyone else.”
Try to share your gigs in social media, but be aware: you should not spam (otherwise you are likely to fall into troubles).
Use the right tags. I can’t stress this one enough. TAGS ARE EVERYTHING. Watch the tags of the most successful sellers who offer similar services to yours, and then copy them.
Use a good SEO title.
Write a good description and a good title.
Set reasonable prices, but do not undervalue your work.
Add a lot of imagines to your gallery (and if you can, even a video).
Add samples of your work.
I hope these tips will help you!