Learn Russian: Нам удалось достичь этой цели, хотя график был очень жёсткий. - We managed to achieve this goal, although the schedule was very strict.

The sentence uses удалось, which is a verb of success meaning 'managed to'. In Russian, verbs expressing success, achievement, or forgetting always take a perfective infinitive. This is because the focus is entirely on the successful result of the action, not the process of trying.

Why is 'this goal' translated as этой цели (genitive case) rather than эту цель (accusative)?

The verb достичь (to achieve or to reach) strictly requires its object to be in the genitive case. Since цель is a feminine noun ending in a soft sign, its genitive form is цели, and the matching pronoun эта changes to этой.

Why is the sentence built as Нам удалось rather than starting with Мы?

The verb удаться (to turn out well or to succeed) works impersonally. The person who succeeds is the receiver of the success, so they go into the dative case (нам). Because there is no grammatical subject performing the action, the past tense verb defaults to the neuter singular form, удалось.

Is жёсткий the normal word for 'strict'? I thought it meant 'hard'.