What is the default "required capability" associated with Slider Menu? If it's something that the Editor role doesn't have, they won't be able to access that menu even if you change it to something else. In effect, with the free version of Admin Menu Editor you can only make menu permissions more restrictive, not less.
This is because the plugin/theme that added the menu usually contains a hardcoded capability check that won't let users without the required capability access the menu. When you change the capability in the menu editor, it changes the capability that WordPress associates with the menu, but it doesn't remove the checks done by the plugin/theme (there's no way to change those without editing the source code).
To let editors access a menu like that, you'll need to assign the necessary capability to the Editor role. You can do this with a role management plugin like User Role Editor.
Alternatively, upgrade to the Pro version of Admin Menu Editor. It has a new role-based permissions interface and will automatically grant the required capability to the roles that you select.