Kinda of like a hyperactive Asteroids... but better.
Okay, I'll start with the controls. The use of the touch screen to aim is excellent, as it allows for good precision. The d-pad obviously isn't the best tool when you're trying to move accurately at speed, but the game seems to detect even subtle changes in direction quite well. If that fails, just fire in the direction you're moving and clear a path!
The gameplay itself works excellently in part due to the controls, but also due to the design of the game. The enemies each have different behaviours, from the pink star that moves around seemingly at random to the magnet that speeds towards you, forcing you to either fill it with bullets or lose a life. These behaviours also help you to choose a strategy, for example if the screen filled with blue chasing diamonds then you might try to get to a point so that they're all coming from a similar direction, making them easier to kill. The level designs, similarly, might make it easier to shoot the green shapes due to a lot of corners to force them into, or harder in general by having barriers. Most of the (numerous) levels also seem to differ in the way enemies respawn. These factors combined make each level different to the last, keeping you on your toes. There is also the drone system. Being able to set a different behaviour is an interesting feature, though I think that the Collect behaviour is probably the best at least when you're not playing levels purely for a higher medal. It means you don't have to worry about collecting the geoms left behind by the enemy, and can focus on just killing wave after wave of spaceship safe in the knowledge your multiplier should be going up (as it is increased by collecting geoms).
I personally don't see why people seem to dislike the graphics. Yes, they're simple and yes the game lacks the background "tears" of its bigger brother. But the graphics do the job perfectly. The colours are crisp and clear, the particle effects look good, your bullets will thud into the perimeter wall and leave small trails from the ricochet. Even though the shapes are simple, it's actually a good-looking game. I think the most obvious way to tell the graphics work is that they don't impede you at any point.
This isn't to say the game is perfect. I personally play the game with the volume off, as the music and effects don't really add to the game for me, though I don't feel they really ever needed to. Also, when an enemy spawns right next to you and hence kills you, it can be extremely irritating, though it can be avoided by noticing where they tend to spawn and avoiding those spots.
The addition of Retro Evolved makes this already-cheap game even better value. Overall, Galaxies is a game that can be enjoyed either in short bursts or for a more prolonged period of time. If you own a DS and want what is simply a fun game to play, you should consider investing in Galaxies.