This is a common problem. Please bear in mind your system config is specific to you so what is described below may not be the answer.
Initially I used a 3rd party app called CNTLM and pointed Eclipse to the CNTLM process port, which points to the corporate proxy but I would no longer recommend this option as it doesn't account for passwords expiring regularly.
I later discovered that Basic Proxy Authentication was disabled by default as part of a JRE 8u111 Update under the heading 'Disable Basic authentication for HTTPS tunneling'. As the document describes, you can override this behavior either 1) globally on your machine if you have the necessary permissions or 2) locally if you have Eclipse installed on a file system you have write access permission.
Try changing your Eclipse.ini file to include this under after -vmargs
Leave your Network Connections set to 'Native'. Only HTTP Dynamic should be ticked
I would not recommend updating from 1.0 to 1.3 because there has been so many changes since then and projects will need to be migrated. It would be safer to try downloading a fresh install following the instructions to install the plugin and then test your 'Check for Updates' button.
Using a fresh workspace is also recommended.
On a different note, you can pass proxy login details into the target url if you encode it properly. I've used this trick for Node Package Manager (NPM) configuration in the .npmrc file
The other common issue you might encounter is the PKIX Path building failed. This is related to HTTPS connections from your JRE running Eclipse and a missing CA certificate from your cacerts certificate store.
Consider logging the issue with WRC if you are looking for a more bespoke solution.