In the Waluigi and Diddy K challenges, try to score as many goals as you can before deliberately drawing the game (shoot into your own goal). This forces a sudden death (or shoot-off).
Since you only need to make one goal to win, use a Mega-Strike to complete the challenge.
For the Striker's Cup, it's recommend having a Dry Bones instead of Koopa or Toad probably Koopa. My team was Yoshi (Mario/Luigi is better), Dry Bones, Toad and Hammer Bros.
Dry Bones can score easily with the skillshot and can score better if you next to the fence and click the Z at least 2 times, then go to the place where the corner kick should be, go in the direction of the keeper and the disappear and shoot, its probably a goal if done correctely.
Toad is good because of jumps, try to pass by the keeper with a jump. You can also go to corner use jump and as soon as the keeper hits you pass the ball and if theres no one at the goal it should enter.
With Hammer Bros. use the hammer when someone is next to you and use the skillshot when near the keeper.
Mario/Luigi is good because of the power-up. Charge the ball and before shooting click on the d-pad (to jump), and repeat this till the ball is white then just shoot and it should be goal. Hes also good at shooting from far with the ball charged.