...
GET http://teamcity:8111/app/rest/builds/<build_locator>/artifacts/content/<path>
(returns the content of a build artifact file for a build determined by <buid_locator>)
<path>
above can be empty for the root of build's artifacts or be a path within the build's artifacts. The path can span into the archive content, e.g. dir/path/archive.zip!/path_within_archive
...
GET http://teamcity:8111/app/rest/builds/id:100/artifacts/children/my-great-tool-0.1.jar\!/META-INF
GET http://teamcity:8111/app/rest/builds/buildType:(id:100Build_Intallers),status:SUCCESS/artifacts/metadata/my-great-tool-0.1.jar\!/META-INF/MANIFEST.MF
GET http://teamcity:8111/app/rest/builds/buildType:(id:100Build_Intallers),number:16.7.0.2/artifacts/metadata/my-great-tool-0.1.jar!/lib/commons-logging-1.1.1.jar!/META-INF/MANIFEST.MF
GET http://teamcity:8111/app/rest/builds/buildType:(id:100Build_Intallers),tag:release/artifacts/content/my-great-tool-0.1.jar!/lib/commons-logging-1.1.1.jar!/META-INF/MANIFEST.MF
...