If you were asked to represent "invincible" or "winning without fighting" in pictures, how would you do it?
For invincible, perhaps a projectile richoceting off some sort of barrier and for winning without fighting I might use a white dove wearing a gold medal
It's a bird, it's a plane, no, it's.. SUPERMAN!
Go for something bold and simple, like the Superman logo! Although this specific logo may have certain associations with invincibility built up over many decades, the imagery of bold logos also has the same, and will inspire the message you're trying to get through.
Also for winning without fighting, personally I'd go the Asian route and try to evoke the martial arts way of looking at it, perhaps with an Asian style font or architecture in the logo/picture.
Although this might end up looking like some brave Noodle shop.. But this is what I'd go for first if given such words to work with :)
Hope that helps some :)
For invincible, a piece of armor or a robot. Anything chromed.
For winning without fighting, a robed man (gives a nod to eastern philosophy, Ghandi, Jesus, less aggressive martial arts, gurus, etc).
Chess pieces? The King? A bit cliché but you can infer winning without fighting as it were. Or not.
A little flag on a mountain top, or the highest step on the podium. Those represent winning and a great feeling of invincibility. I see it as winning a competition like crossing the finish line on first. To me, winning and be invincible means to be the first... I hardly see how you can win without «fighting» at least against yourself, in a non violent way though...