Get Jenkins artifacts URl from REST api
If you're using the ArtifactDeployer Plugin, then, unfortunately, the artifacts deployed through it won't be listed by the API.
The ideal solution, if you have the time for it, would be to mod the plugin and add an API to it.
In my case, due to time constraints, I had to scrape the page instead, by fetching the build's HTML page and picking up all the <a> tags whose href started with "deployedartifact/downloads".