This isn’t easy. This may help: http://www.cinqueter…
“Best” is probably train or bus (perhaps faster????) to Nice and train from there, but the process will take all day. The fastest train from Aix to Levanto is just over 8 hours with 2 connections. This will probably be fairly scenic, but it’s still all day on trains and waiting for connections on train platforms.

I’d seriously look at taking the Chemins de Fer de Provence narrow gauge, scenic line to Nice. It adds some complications but not just a ton of additional time. The views are reported to be magnificent and I’ve always wanted to take this train. http://www.trainprov… You’d have to take the bus to one of the stops (Digne?) and it’s a 20 minute walk between the two train stations in Nice.