Required capabilities

Could you elaborate on what settings you’ve tried so far, specifically?

In general, the capability field works as an extra filter that sits on top of default menu permissions. If the default required capability is “edit_posts”, only users who have that capability will be able to see and access the menu. If you set it to “editor” instead, only users who have both the “edit_posts” capability and the “editor” role will see it.

Note that you can’t completely get rid of the default capability requirement (in this case, “edit_posts”) because it is usually hardcoded in WordPress or the plugin that created the menu.

One unfortunate side-effect of the above is that you can’t give a role access to a menu that it couldn’t already see. If the original capability is “manage_options” (only admins have that) and you change that to “editor”, it just restricts menu permissions further. Editors still won’t be able to see it because they don’t have the “manage_options” capability.

To give an editor access to a menu, you’ll need to give them the required capability that’s associated with that menu. You can use any role editing plugin for that, e.g. this one:
https://wordpress.org/plugins/user-role-editor/

(The Pro version of Admin Menu Editor simplifies the process by automatically giving the necessary capability to selected role when you enable a menu item.)