What kind of surgery/procedure/remedy is recommended to fix my negative canthal tilt? (Photo)

you photos are good from the front. But a lateral is really necessary as well as an exam of your jaw and teeth to determine proper treatment. A canthopexy is needed but maybe bone surgery as well with cheek bone advancement or augmentation. An in person exam is needed to really know the proper approach. 

bee1990,You have multiple options to address the downsloping lateral canthus, though surgical options vary a great deal, and should address not only the eyelid, but also must be done in the context of your facial exam, as your bony anatomy as well as your soft tissue anatomy must be taken into consideration when making a surgical plan.  Good luck!

Dear bee1990, Lower eyelid surgery to reposition the outer (lateral) part of the eyelid more superiorly (lateral canthoplasty or lateral tarsal strip procedure) may be the appropriate procedure for you but a formal consultation with physical examination is needed for this determination.  Lateral canthoplasty may make the eye opening (palpebral fissure) noticeably smaller in patients with upper eyelid drooping (ptosis) even if mild...Best, Dr H

The side of the eye may tilt downwards and sometimes people wish for this to be corrected.  Options would include cathopexy (repositioning the tendon that supports the eyelid into a more superior position) or even implants or bony surgery.
I would recommend an evaluation with a board certified plastic surgeon to determine the best course of action for you.

Downward slant of the lateral canthus, antimongoloid slant, needs a full examination. Can be corrected by a canthoplasty procedure.

From your photo, it appears that you will benefit from a lateral canthopexy.  You have a little excess skin on your upper lids as well that could be taken care of at the same time.  Good Luck.