Learn Russian: Проект казался невыполнимым, но команда всё-таки добилась успеха. - The project seemed unfeasible, but the team nevertheless achieved success.

Placing всё-таки directly before the verb добилась focuses the "nevertheless" firmly on the action of achieving. You could place it right after но, but putting it before the verb is highly natural in written Russian to highlight the unexpected success.

Why is the adjective невыполнимым in the instrumental case?

When an adjective describes a subject via a linking verb like казаться (to seem), являться (to be), or становиться (to become), it typically takes the instrumental case. Here, it describes the nominative subject проект.

Why do we say добилась успеха instead of using the accusative case успех?

The verb добиться (to achieve or attain) strictly requires its object to be in the genitive case, not the accusative. Therefore, the masculine noun успех takes the genitive ending and becomes успеха.

How do the verb aspects work together with всё-таки in this sentence?

The imperfective verb казался sets the background scene of an ongoing, doubtful state. The perfective verb добилась delivers the final, completed result. The particle всё-таки bridges them, emphasizing that the completed result happened in direct defiance of that background state.