Space Invaders Infinity Gene

A Nagoya Attack is when an enemy bullet passes through your ship without it hurting you. You unlock this ability through the evolution tree, likely during stage 2. The best place to do this that I've found is the boss at the end of stage 2-3 "Preadaption". Once you've unlocked Nagoya Attack, go to this stage.

This boss simply moves back and forth firing huge waves of bullets at you, so just go up to the top of the screen, directly underneath it, and follow it back and forth. Don't shoot it, just wait for it to self destruct. You should get 100-200 Nagoya Attacks easily each time it fires a volley. I ended up with about 1850 total by the end, so there's way more than enough here. :)

Simple, just go to Bonus stage 1.1 once you have unlocked the Nagoya attack and follow this video.
There is also an oppotunity at the end of stage 2.3 but I believe this to be much longer.
Credit goes to KingSuperOne for the video

To successfully get this achievement, you first have to have unlocked the ability to pass through enemy attacks for the brief second when the shots are first fired, or "Nagoya Attacks".

The way I did this was to find a level with a UFO that shoots a shower of lasers (Bonus 1-1 has one). You will have to follow him from left to right and try to "catch" his fire. Position yourself right under the UFO so that his shots pass through you. Do not shoot at him before you get 1000 Nagoya attacks come up on screen. With each shower of lasers he produces, you should be able to get 120-170 Nagoya attacks at a time if you're in the right position.

Once you have a 1000, shoot him down and then you will need to get to a game over screen, or finish the game, for the achievement to pop.