Learn Finnish: Sinun täytyy väistää kaikki iskut.

Because of the verb täytyy (must). Verbs expressing necessity require their subject to be in the genitive case. This structure is often called a "necessive sentence," and you can think of its literal meaning as closer to "of you it is required to..."

Since this lesson is about the negative participle, how does the -maton/-mätön suffix apply to the verb väistää?

If you add the negative participle suffix to the strong stem of väistää (to dodge / avoid), you get väistämätön. This literally translates to "undodgeable" or "unavoidable," and it is the standard Finnish word for "inevitable." So, an unavoidable attack would be väistämätön isku.

Why is the object kaikki iskut (all attacks) in the basic nominative plural form rather than the partitive?

Because the action is complete and bounded—you must successfully dodge all of the attacks, not just an undefined amount of them. For total objects in the plural, Finnish always uses the nominative plural (ending in -t). Notice that while singular objects drop their accusative -n ending in täytyy sentences, plural objects just keep their normal nominative plural -t form.

Why doesn't the verb täytyy conjugate to match the subject?