So I've been doing SEO for quite a while and have had some really good success. The problem I'm facing is how to show these successes on my Web site portfolio.

Any ideas

Charts, graphs and so on! Showing lines going up. 

Pretty obvious, I know, but you can now make some nice interactive features using the free Google Data Studio tool, which you can then embed. There are also many other free and paid tools.

I'd concentrate on the simple things: increases in SERP position, increase in visitors, and increase in revenue for the people you work for.

Not specifically visual but writing some case studies might be beneficial?