Travel to any Diricawl Den you know about, or head to the one the quest marks for you. A den near Hogwarts is shown in the image below. Cast Levioso on any Diricawl at a den and use your nab-sack to capture it.
Travel to any Giant Purple Toad Den you know about, or head to the one the quest has marked on your map. An easy-to-access Den is shown in the image below. Similar to the Diricawls, cast Levioso on any beast and use your nab-sack to capture it.
Attend Beasts Class during the day
After capturing the two beasts, head to Beasts Class and wait for it to be daytime if necessary. Beasts Class can easily be reached by the Beasts Class Floo Flame in the Bell Tower wing.
Return to Professor Howin
Once the class cutscene ends, talk to Professor Howin to complete the quest. She will teach you Bombarda, a powerful explosive spell that can destroy obstacles and damage groups of enemies.