Getting from Astrakhan, Russia to Aktau, Kazakhstan

I'm in Astrakhan, Russia. There's very little information out there on buses or trains to use to eventually get to Aktau, Kazakhstan.

bahn.de shows a 75 hour train with 3 changes, so I have no idea what crazy route that's taking as it's really not that far.

I think in theory I can get to Atyrau first, and then a connection from there to Aktau, but this is all in theory only; I may just have to wing it when I get there - unless you guys can help with some more info? :)