There's an easier way to do this trick than using the Triple Dip, and it doesn't require any items, but you must have the badge that gives you the "Mega" hammer move (the exact name escapes me), and Bombette must be Ultra-ranked.
The trick is, with Bombette as your partner, to corner the Amayzee Dayzee on the overworld so that its not moving, then set off Bombette with C-Down so that she explodes on the Dayzee. You'll get a preemptive strike and do about 6 points of damage. Then, have Mario hit the Dayzee with the Mega hammer move to do 9 pts, and follow up with Bombette's Ultra bomb technique to finish it off. There's no way, provided that you don't miss any action commands, that the Dayzee can either hit you OR run away before you kill it. I know because I just did this today ;)
Quasar