Well, midget16, as goron said, don't touch the fruit. It's not possible to die in the early levels if you don't touch the fruit (unless you take too long and the fireball comes up, but until you get to 16 that shouldn't be that big a problem)
I had to play A LOT to get as good as I am at the game now. And I STILL die on the early levels at times just because I'm rushing to get to the next level.
Yes, you are on a time limit, but while you're moving, look at the level, or better yet go to one of the sites that lists all the levels and study them there. Remember the patterns of the fruits, where they go usually, and how they attack (especially important for tomatoes)
A lot of these things take time. This is a game more suited to people who can or have played the original Mario Bros. If you haven't, I'd suggest finding an old NES system and the games at a thrift shop and practice them

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