Learn Arabic (Modern Standard): الاجتماع ثلاثون دقيقة.

In Arabic, numbers from 11 to 99 are always followed by a singular noun. Even though we translate it as "thirty minutes" in English, the Arabic literally says "thirty minute". You only use plural nouns for numbers 3 through 10.

What case ending does دقيقة take after the number 30?

It takes the accusative case, which means it ends with an "-an" sound (دقيقةً, daqiiqatan). Any noun counted by a number from 11 to 99 must be both singular and accusative.

I've also seen "thirty" written as ثلاثين (thalaathiin). Why is it ثلاثون (thalaathuun) in this sentence?

Tens (20-90) change their ending based on their role in the sentence. Here, ثلاثون is the predicate (the core information about the subject, الاجتماع), so it takes the default nominative ending "-uun". You would use ثلاثين (with an "-iin" ending) if it were the object of a verb or came after a preposition.

دقيقة is a feminine noun. Do I need to change the gender of ثلاثون to match it?

No! Unlike numbers 3-10, the "tens" numbers (20, 30, 40, up to 90) do not have separate masculine and feminine forms. ثلاثون is used exactly as is, whether the noun following it is masculine or feminine.