Learn Hardcore Swedish: Hon förtjänar mer tid.

Because tid means time, and in this sentence it is an uncountable noun. In Swedish, mer is used with uncountable nouns, while fler is used with countable plural nouns.

mer tid = more time
fler timmar = more hours

So Hon förtjänar mer tid is correct.

What form is förtjänar?

Förtjänar is the present tense of the verb förtjäna, which means to deserve.

A few common forms are:

infinitive: att förtjäna = to deserve
present: förtjänar = deserves
past: förtjänade = deserved
supine: förtjänat = deserved

So Hon förtjänar mer tid literally follows the pattern she deserves more time.

Why does the verb end in -r?

In Swedish, many verbs in the present tense end in -r. That is the normal present-tense marker for a large group of verbs.

For example:

jag talar = I speak
hon arbetar = she works
han förtjänar = he deserves

So the -r in förtjänar is just the normal present-tense ending.

Why is there no word for does or is in the sentence?