Weaknesses and imperfections humanize a person. If you want a character to seem almost mythological(and they will have this kind of impact on your story, whether you like it or not), a good way to go about it is to not show their weaknesses.
However, realistically speaking, everyone has their weaknesses. Zeus was into mortal women and a major cheater, Achilles had his legendary tendon, Midas was greedy and so on - a character's dramatic and narrative potential is ultimately decided by their faults, not their strengths. Not giving them a weakness might make readers feel indifferent towards your character. Again, if this is purposeful, then great. If not... well, not every weakness needs to be major. The weakness could be introversion or a general dislike of human contact, or the incapability to understand large concepts or even a lack of patience... Anything goes, really. Be creative.