For the Minus Zero achievement, you have to reach the part in Level 5 where the music changes. To be honest, I reach this part many times and the achievement didn't unlocked. However, during one of my attempt, I reach Level 5 and had to go eat so I put the game on pause. It seems that the achievement have unlocked during this time.
For the Young man achievement, you need to get a gamer age of 19 or below. I got a score of 403K and still had 20. It's the average level rating for the 4 major shmup skill test that count. I finally reach an age of 19 after getting Level 100 on the 8bit game, 100 on the bullet evasion, 75 on the balls evasion and 100 on the asteroids. The score doesn't really matter, aim for the best level.