Instagram photos will show up in your Twitter feed as a full image rather than a link then also be saved to Dropbox. Note: only works for single photo posts.
Then
Post a tweet with image
This Action will post a new tweet to your Twitter account with a linked pic.twitter.com image. NOTE: Please adhere to Twitter’s Rules and Terms of Service.
And
Add file from URL
This Action will download a file at a given URL and add it to Dropbox at the path you specify. NOTE: 30 MB file size limit.
Explore more great ways to automate Dropbox and Twitter