Since your robot, Bill, can only beat three other robots (Fireball, Necromancer, and Thunder), it is important that you face one of those three in each round of the tournament.
If Bill faces any other robots, you’ll lose. But it’s not immediately clear the order in which Bill should face these three. In order to decide, notice that one of these robots won’t face any other robot but yours, one will face just one other robot, and the last will face two other robots before yours. So let’s take a look at which robots these three can defeat.
At first glance, it seems as though each of these three robots could fit into any tournament slot. Notice, however, that each can defeat one of the others (Thunder can defeat Fireball, Fireball can defeat Necromancer, and Necromancer can defeat Thunder).
This doesn’t help us win. If any two of these robots face each other, one of them has to lose, and then there won’t be enough robots we can beat left in order to win the tournament. Since we don’t want these robots to face each other, we can ignore their chances against each other.
This means that Necromancer must be the last robot Bill faces, since only that robot can defeat two others. Plus, notice that both Thunder and Necromancer can defeat Xplosion, but Xplosion must be one of the two robots that Necromancer needs to defeat to make it to the last round. This leaves no robots left that Thunder can defeat, making Thunder the robot Bill will face first, and Fireball the robot bill faces second.
Thus, Bill will defeat Thunder in the first round. Fireball will also defeat Chainsaw in the first round, after which Bill will defeat Fireball in the second round to make it to the championship.
Necromancer will face off against Atomizer and Xplosion, but in which order? Similar to the other division, one of those two robots will be immediately defeated by Necromancer, while the other robot must win a match before moving on to face Necromancer in the second round.
The only robot left is Slammer, and only Xplosion can defeat Slammer. Thus Necromancer will defeat Atomizer in the first round, while Xplosion will defeat Slammer. Then Necromancer will defeat Xplosion in the second round to face Bill in the championship.
Since your robot Bill can defeat Necromancer, Bill can win the tournament if it is seeded exactly this way.