Description taken from Arcade version of this game

Asteroids Deluxe is the 1980 upgrade of the classic 1979 Arcade smash hit Asteroids. In this edition, your job is the same: pilot a small ship through an asteroid field, destroying the space boulders as you go. In addition to the asteroids, you will face a menacing flying saucer and a mysterious alien cube. Players start with three ships at the outset of the game, and additional ships are awarded at point increments of 10,000.

In Asteroids Deluxe, the power of hyperspace is gone, replaced by a shield that protects you from asteroids and alien crafts, but the number of hits it can take is finite. Your ship still has the thrust capability, which can get you out of danger in a bind. Like its predecessor, the playing field in Asteroids Deluxe is swarming with asteroids. The large ones break into two medium-sized asteroids, and the medium ones break into two smaller ones. The smaller the rock, the faster it travels.

Occasionally, a flying saucer appears from the side of the screen to fire missiles sporadically in every direction, destroying asteroids and your ship if you are not careful. The saucer moves in a straight line on some occasions and in a random pattern at other times. The saucer is destroyed if it collides with an asteroid. The mysterious cube also appears from the right or the left and floats lazily from one side of the screen to the other. If shot by you or the flying saucer, it breaks into four ships that focus on your ship and attack. Moreover, each of the four individual ships breaks into two more ships when shot to create as many as eight swarming ships attacking you at a given time. ~ Anthony Baize, All Game Guide