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!

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.