Learn Russian: Без гибкости тяжело делать эту растяжку. - Without flexibility, it is hard to do this stretch.

It replaces a full conditional subordinate clause. Instead of saying a longer phrase like Если ты не гибкий (If you aren't flexible) or Если у тебя нет гибкости (If you don't have flexibility), the sentence uses the preposition без plus the noun гибкость. This compresses the condition into a single, efficient prepositional phrase.

How does the word растяжку fit into the concept of verbal nouns?

Растяжка is a verbal noun (отглагольное существительное) derived from the verb растягивать (to stretch). Instead of describing the action of stretching with a verb clause, Russian packages the action into a noun. It is in the accusative case here (эту растяжку) because it is the direct object of the verb делать.

Could we use the adjective тяжёлый instead of тяжело here?

No, because this is an impersonal construction. There is no grammatical subject for an adjective to agree with. When expressing that it is hard to perform an action, you must use the adverbial form тяжело or трудно paired with an infinitive, which in this sentence is делать.

As a quick refresher, why does гибкость change to гибкости?