I have been archiving many of my favorite tumblr's for some time now, but will have to go in and refresh my downloads.

Highly recommend this app called TumblThree for archiving (also TumblTwo) https://www.jzab.de/content/tumblthree

The UI is a little annoying and takes a little discovery to figure out, but the actual setup / install is painless.

Edit: after reading more about the shutdown, it appears Tumblr may have their own export tools, they could be superior if you are exporting your own content, I'm not really sure.