The Real Ghostbusters game was developed by produced by Activision for the Game Boy in 1993. This is not related to the The Real Ghostbusters arcade game released by Data East. This game has Peter Venkman solving puzzles and avoiding ghosts.
To advance to each new stage, the player had to collect stars, which would open the door to the next level. The proton gun was effective only on blocks at the character's feet, not on the ghosts (bombs were used to destroy the ghosts). If the player lost all his health (by touching damaging things like ghosts, flames, and reforming blocks), or the 999 second timer wound down to zero, the player would lose a life. After successful completion of a level, the player would be rewarded with a 4-digit password, which would enable them to start at the end of that level next time they played (the game had no save feature).
The Real Ghostbusters game was the third of three games released by Kemco based based on the same gameplay. The other two games "Garfield Labyrinth" (first of them released) and "Mickey Mouse IV: Mahou no Labyrinth" are basically the same game with some different sprites. The games are part of the Crazy Castle series, which lists theses as the collective fifth entry.