Here you will find tips on battling every enemy and Boss in Cave Story (not counting Wind Fortress) Thus, it will be noted that this may be a spoiler, depending on how far you have made it into the game.
This page is currently incomplete, but I will be working to finish it.
Before you can fight at all first you will need to find the Polar Star. Once you do, start taking down your enemies. Even though they are all very weak at this point, you only have 6 health, if you have obtained the Life Capsule, so they do pose a threat.
These particular bats only fly a fixed distance up and down, regardless of your position, so they are not dangerous. The safest way to take them down is to line up with a point on their flight path, and constantly fire. The quickest way is to wait until they start to fly up, run under them, and rapid fire up. Even a level 1 Polar Star will work.
These guys are more dangerous than the bats. Once they see you, they will hop towards you, upon contact dealing one damage. The best way to fight them is to shoot at them from level ground, dealing at least two damage, which will kill them. If they end up jumping, try to hit them from underneath, or just back up, and fire again. A level 2 Polar Star will handle this quite well, as it will eliminate them instantly. If you encounter a pack, you can deal with them one at a time by creeping up to only the foremost Critter; or, if you want to, go at them all at once. Fire horizontal shots whenever you can, and fire up at those above you. (Don't forget to get out of the way if you don't kill a falling one!)
The door is interesting. Just don't go on its platform (or it will deal you 4 damage) and fire (you will have to jump) from afar.
You will notice that Mimiga Village is a peaceful place, but that is going to change. It would be worth while to fully level up you Polar Star, because you will have you first boss fight here. (You may have to let the enemies in First Cave regenerate to get enough crystals; To accomplish this, go in and out of the save room door or the gunsmith door.)
Eventually, you will encounter Balrog and Misery. They are attempting to kidnap a Mimiga named "Sue." Balrog will ask you if you want to fight, and you could say no, but where's the fun in that? You are in a small space with one, small suspended block on the right. Get ready.
Now his name sounds intimidating, but don't wory; when you see him you will be pleasently surprized.
His attack pattern will be to charge at you, then leap, dealing damage if he ever touches you. Also, if for some reason you are right next to him on the ground, he will grab and fling you, dealing some damage.
The best strategy for fighting him is to fire as he charges, and run under him as he leaps, firing up. If you notice he is not leaping, he is going for a grab, so jump out of the way (the block will come in handy) and be careful not to run to early, or you'll just bump into him.
Found in the Graveyard, as his name suggests, this enemy is going to be a little tricky.
The Graveyard is full of Pignons, so wait untill the Grave Keeper has moved to the other side away from you, then hop down and eliminate as many as you can, before dealing with the Grave Keeper.
His is impervious to all you attacks, except when his sword is raised. Wait until he gets to you, then back away and fire. If he corners you up against a wall, jump over him, giving you much room to work with.
This is a lab which is experimenting with dragon eggs. There are lots of weird things here (including the English language.) alongside decently hard to navigate terrain. Don't forget to look for life capsules and weapons.
These guys look like elephants, deliberately attack you, that is, until you aggravate them. They are not really dangerous, just stand next to their pits and fire. They will go wild but cannot hurt you.
If you think they are just to cute to kill, just hop from the pit edge to one of their backs and ride them across.
Unlike other enemies, most beetles here are not stationed at specific locations. Instead, when you walk into specific zones of the Egg Corridor, a swarm of Beetles will appear. This can occur indefinitely, so be prepared to fight another swarm if you move back into the zone.
They are not dangerous individually, but a swarm can be annoying. They will fly directly towards you at all times, and can pass through certain walls, adding another threat, since your shots will stop at the wall. They will likely come at you from a diagonal, where you cannot hurt them, so it is necessary to be level or directly under them. Do not stay in one place, however. You should move constantly to ensure they do not get to you, but in so doing, be sure to plan ahead so you do not become cornered. Because they can pass through walls, you may find them coming from the ground you stand on. If this happens, run to the side, and shoot when they emerge.
Some beeltes patroll allong a specific line, instead of swarming you. To eliminate them, just wait till they move away, and jump down to their ground and fire at them. To make collecting their drops more easy, you can also jump down directly above them and shoot down. (This is only better, of course if there is a platform under the beetle.)