Clear out the Dementors in the middle then go up to the Dementors that are sucking the soul out of Sirius and attack them. The health meter at the bottom will go down. Keep attacking until you defeat it. Do this quickly, as Sirius only has a bit of health.To defeat the Dementors in the first stage (where you drag Sirius Black), do not wait until the Dementors are sucking the soul out of Sirius. Hit any of them that edge closer with Expecto Patronum. After a few hits, the first stage will be over.

The second stage of the Dementors is much more difficult. There are many more. Shoot Expecto Patronum at the Dementors (do not power up as Sirius will get weaker), and press X to charge at them. Break through the crowd in the back. Once you have a path cleared, go for the Dementor attacking Sirius. Power up until it automatically shoots. Remember to press X to charge and go faster. If you take too long the Patronus will die down.