Chapter 1. This achievement is missable.
The Mega Phobetor arcade game is in the Stardust Club, which you will visit first during Chapter 1. This will be available to play until you begin Chapter 5, and will also be available in the Endless Christmas chapter. When you enter the Stardust Club, go right two screens to the game room and you will see the Mega Phobetor on the left. Select it and select the right Hand icon to play the game. You must reach the end of the game and defeat the final boss to unlock this achievement.
Good news and bad news. The bad news is that you must try to hit every enemy quickly as soon as they appear, and don't miss any shots, as there is a multiplier and this will increase your score a lot, which is needed to unlock the boss. The good news is that the game is exactly the same every time you play. This means that with some patience and practice, you can memorize the enemy pattern and know where to shoot before they even appear.
There are different sets of enemies that appear, from eyes to mouths to ghosts, along with power ups for your health and your charge (ammo). You can quickly grab the power ups in between shooting the enemies, but be quick as they disappear after about a second. There is a certain point within the game when you see a series of eyes appear from the top to the bottom in each row, from left to right. At the end of this sequence, you must have reached a score of 50,000 to advance to the boss stage. If you don't do well in the beginning and miss some enemies or miss some shots, you may find that you finish under the 50,000 score mark. But, as you keep playing and keep the multiplier going, you'll be able to hit just over 90,000 at the end of this sequence, easily unlocking the boss level.
The boss is basically a big head and he will flash a few times on the screen before materializing in a solid form for you to shoot him. I actually shot him while he was still flashing in the spot that he was just about to materialize in. It would hit him and he would disappear and go to the next spot. I continued hitting him while he flashed, just before or as he would solidify. After a few shots with him, you will go through a few more sequences with enemies such as falling eyes and moving mouths. Be really quick to grab the power ups to keep your health and charge as full as possible, while killing all the enemies on screen. Eventually you will get a power up in the dead center of the screen for infinite charge (ammo) so fire away at him. When you see the animation of his face changing into a monster, you have defeated him.
Achievement unlocked! 💚
Also, here is a quick video of the Mega Phobetor including the boss defeat. All credit to DoaneZone Gaming for the video.