Plugins generate menu items by calling add_management_page(). Here they insert the slug that ends up in the menu. Usually this slug is the same as the plugin slug, but this is not mandatory. Hence your partial result when you tried this. You would have to scavenge all plugin files to find the slugs as @Mark Kaplun suggested.
Or you could override add_management_page(). Make sure your plugin is loaded as early as possible (use add_action('muplugins_loaded', 'your_plugin_name',0);), so all other plugins will use your version of add_management_page().
Using PHP’s debug_backtrace you can find the function that called your version of add_management_page(). Next you can find the path where that calling function originates with PHP’s ReflectionFunction. Then you match the path with the list of plugins you got using get_plugins(). This gives you all the information you need for your tooltip.
So, it’s a hell of a job and I certainly didn’t try it out.