How do I beat last boss battle?

Well to beat it, just use fireballs and Bowser will eventually get knocked out of the bridge but if you don't then there is what's what:
Bowser has 3 attacks that all consist of fireballs:
1) Bowser simply shoots it out of his mouth (just jump over it)
2) Bowser will jump up a bit and shoot out a fireball (jump over it)
3) Bowser will shoot out 5 fireballs that are spread out from bottom to top (there is a decent sized spacing between the bottom and the fireball on top of the bottom for you to jump past it)

If your Mario cannot shoot fireballs at Bowser then you'll have to jump at the red switch at the right hand side of the screen. The only was to get past Bowser to do that is to wait for him to do a big jump (not attack number 2) and dash under him. You might want to evade all his attack so you will get to know when Bowser does that big jump (he crouches before jumping). If your Super Mario (2 hits before KO), sacrificing 1 damage to run past Bowser won't work as Mario will get knocked down and won't be unable to move for a period of time.

There is also a Super Guide if you don't get what I mean.

Be sure to pick up a propeller suit during the boss evasion portion- that way you won't have to worry about falling into the magma should you miss a jump on the moving platforms. If you're still having problems- there are a lot of ways to leech extra lives in this game (some of the hint videos show these).

Oh you mean bowser,well you enter his big extreamly noticeable green door,then theirs a hallway with fireballs coming out of the side.all you half to do is doge them by jump,ducking,and running.next you see dunb old bowser,wait till he leaps up high and press the butten,or swith,or whatever it was,then when you think it's all over.the person you think is peach,then you reach her,then you realize its just majickoopa diskised as peach,then the imposter uses his majic stuff to bring bowser back to life,he is 10 in a half times bigger!!!now at this part i hope you got a propeler head,you might need it.so you run from mega bowser but the good news is,the mario seeking fire balls from bowser crush those old walls to make a pathway.their are some rooms with coins,a power up,and stuff.just take advantage of the fire balls from bowser and i think you will do fine...

The first part, when he's normal size:

If you're Fire Mario then you can shoot about 20-25 fireballs at him, he'll drop out of the screen, go hit the big ! button at the end.
If you're NOT Fire Mario then you have to wait until he crouches and jumps to the top of the screen. Try to run under him so you can hit the ! button.

The second part, when he's about 30x bigger:

You have to wait for Bowser to fire those humongous fireballs at you. Once he does, jump over the fireball and let the fireball break the walls so you can get through. Keep letting him destroy his own walls. Ride the moving platform up so you can lead the fireballs to the ? blocks on top if you want. Grab the coins if you wish. After a while you will get to a platform that slowly moves to the right and down a little. Hit the ? block and grab the Propeller mushroom -- it'll help a lot. Ride the moving platforms or let him destroy his walls again. Sometimes he will kind of punch the lava and make it rise into a little wave. Avoid the lava at all costs, it'll destroy you. Use the Propeller power-up to soar up and away from the lava. After some more jumping across moving platforms, you'll find a big switch and the REAL Princess Peach in a cage. HIT IT TO WIN!