Nemesis, despite it's name, is part of the Gradius series of shmup games. This one in particular was the first one for a portable system, the Game Boy. It combined elements from Gradius and Gradius II, as well as some all-new features. The game was released in 1989. They did not bother to change the name back to Gradius something-or-other for it's worldwide release. It is not a scary zombie monster from the Resident Evil series.
You control a spaceship with which you use to fly through space and several different types of terrain, blasting at spaceships, aliens, organisms, and armaments. You collect power-up pods that you can use to activate power-ups such as speed, bombs, double-shots, lasers, options, and shields. At the end of the level there is a boss creature that you must defeat to continue on to the next level.