The Super Mario Brothers theme is on the more challenging side rhythmically with a lot of notes on the off beat. It can help to figure out tricky rhythms by grouping notes into their respective beats.
For example, in the first measure beat 1 has the first two eighth notes, beat 2 has an eighth rest and an eight note, as does beat 3, and lastly beat 4 has one quarter note.
Breaking up the music this way can be a very useful tool in figuring out tricky rhythms. If you're having trouble, try breaking up the rest of the music in this way, and then try counting the beats and clapping the rhythm.
Luckily, it's a very famous tune and most people know how it goes! So chances are you're a pro at the rhythm already, and only need to follow your ear!