Pretty sure DROP PROFILE is a system-level access right. It is used to actually drop profiles from the system. In other words, it does not have an "ON" clause.
GRANT DROP PROFILE TO Admin_User;
Also, I couldn't find it specifically in the documentation, but I do not believe you can specify "ON PUBLIC" for grants.
Note: In Teradata 13.10, you need DROP USER on a user to modify them... I believe this has not changed in TD 14.10. Yes, this means your admin user must have an explicit DROP USER privelege on every user it should be able to modify.