Must the actor intend the injury?
No. The actor does not need to intend the injury, only to bring about the consequences that are the basis of the tort.
For example, Δ intends to push π and does so. π falls and breaks his neck. This is a battery. The consequences that are the basis of tort are the harmful or offensive contact to π. Δ intended to bring about the harmful or offensive contact to π; thus, Δ will be liable even if he did not intend to break π's neck.