Learn Farsi: دستیابی به این هدف خیلی سخت بود.

Even though English just says 'reaching this goal,' the Persian verbal noun dastyâbi (achieving/reaching) keeps the preposition of the verb it comes from: dast yâftan be (to attain/reach). Whenever you use this noun, you must link it to the target with be.

Could I use the long infinitive dast yâftan here instead of the noun dastyâbi?

Yes, you could say dast yâftan be in hadaf (to reach this goal). Both are grammatically correct as the subject of the sentence and both can follow phrases you are learning in this unit. However, using the verbal noun dastyâbi is a very common and natural way to express 'reaching' or 'the achievement of' in Persian.

Why isn't there an Ezafe on dastyâbi to connect it to in hadaf?

Because the preposition be is already doing the connecting. Ezafe is used to link a noun directly to its modifier or possessor. Since dastyâbi requires a preposition to introduce its target, the Ezafe chain is broken, so you cannot use one here.

How is the noun dastyâbi built from its root verb?

It comes from the compound verb dast yâftan (literally 'hand finding'). To form this noun, Persian takes the noun part (dast), the present stem of the verb (yâb), and adds the suffix -i to make dastyâbi, meaning the act of attaining or accessing something.