Like a lot of Looney Tunes based games, Daffy Duck: The Marvin Missions is kind of long and tough, due to several factors.
You do get to buy some powerups, but your initial cashflow leaves a little to be desired.
But what you could do, would be to start a new game, and when the title card comes up, quickly press
Left, Left, Right, Right, Up, Down, Y, A, B, X
Done right, you'll hear Daffy say: "Mother..."
Now when you go to your initial purchasing screen, you'll notice that you have lots more dollars at your disposal, you have lots more lives to play with, and you're at the maximum on your 'nutty attacks'.
Which should make the game much easier.