In the freeware version the character on the title screen changes depending on the time, and the music changes as well. Six minutes is the cutoff, if you get under that you should get a new character on the screen. I'm not sure if the 3DS version(s) are different though.
As for tips, try using different weapons to suit your playstyle. The spur isn't necessarily the best choice. For example, the snake is really good for clearing deleets (the exploding wall enemies) before you actually have to pass them.
Don't worry too much about avoiding blocks in the second room. Try to avoid them if you can, but don't stop in one spot or go backwards too often.
Taking minor damage intentionally can help get through certain areas, such as the small spike-filled area surrounded by mesas on the lower part of the third area. It's a bit faster than the alternate route of going to the top of that section and waiting for the deleet to detonate.
The butes in the heavy press fight can be good for gaining health, but you may lose more than you gain if you get hit and it wastes a ton of time.
When the heavy press is defeated, you can hurt yourself on one of the butes and then stand underneath the heavy press. It's faster than waiting for the heavy press to fall then jumping in after it.
Other than that, make sure to save and level up your missiles and keep your life pot as long as you can.
Unless you really need to, don't go into the statue room. You'll waste quite a bit of time that way.
Once you get to Ballos, what I like to do is stand underneath his head and mash the attack button using the nemesis to annihilate his first form. You may need to use the life pot if you don't have any health here.
Second form is pretty easy as long as you have missiles, just try to save some for the last form.
Third form...just try not to get hit. It packs a punch.
An amazing way to save time on the last form is to damage yourself on the spikes, then booster up onto the boss where his left eye is. Stand in the eye. As soon as the boss starts to attack you, hammer it with whatever missiles you have and the rest of your weaponry if you run out.
