Please note: all credit goes to Fae!
I am terrible at arcade games but with this advice I became an ARCADE MASTER at Super NASU!
Try standing near or in the corner and holding down the autofire button while dodging every now and then. The autofire button is X on an an Xbox 360 controller or space on the keyboard.
If you stand directly next to the corner your autofire will shoot the bird in a way that makes it impossible to get the eggplant. Standing a little bit away from the corner should help with this. Try to get as many eggplants as possible as they restore half a heart but don’t take unnecessary risks to get them. Every three purple eggplants grants triple shot and golden eggplant gives you triple shot instantly.
Stay near the corner area as much as possible the middle of the map is the most dangerous place to be. While in the corner you only need to keep track of the objects heading towards you which makes things more manageable.
It should take a few tries but eventually you should eventually be able to get it with perseverance. After you get 5000 points you will get the Arcade Master achievement.