Folowing on Milo’s comment, do_shortcode expects the parameter to be exactly as if it is a shortcode inserted as part of the content, therefor your attempt to quote avatar_upload is just wrong and it should be do_shortcode('[avatar_upload]');
In addition it is probably better to just avoid using do_shortcode and call the relevant official API, if the plugin has one, directly, especially since shortcode might be processed differently based on context, in a way that might not match your needs.