The actual weapon, you can get that after 4 wins.
The sigil however, you can win it in a tournament, after you've won all of his overdrive reels, so it depends on how fast you win the sigils.
A nice trick is, to save BEFORE you know what the tournament prizes are, and then look, if there isn't a reel, then reload the save and look again, over and over till there is a reel, then play it win it, and so on.