Unfortunately that is not possible for fields. ALM does not at this time allow for the edit of existing tool tips (mouse hover) nor for the addition of new ones in relation to fields.
You can add new menu buttons and add tool tips (hints) for those, but that is the only area of ALM where you can add new tips for mouse hover. Several enhancement requests have been submitted to HPE asking for such, but so far they have all be deferred.
As you mentioned requirement field explanation, I have seen some users use the Rich Text Template area of the Requirement Types customization to enter in explanation text for custom fields. Both existing and new requirements would have the rich text area available to click to. Would require you instructing your users to know to look there. Easy way to keep explanation detailed text in the same area of focus as it would be in the requirements details window. Just would need to click over. Possible workaround since you at this time cannot add any tool tip information for fields.