1. To attack vigorously or violently: "The troops are assailing the terrorists."

"It is difficult to believe that Mike could be assailed by so many bad things; he lost his job, his wife became very ill, and the roof of his house was damaged by a storm that caused severe leaks when it started to rain."

2. To attack with arguments, criticism, ridicule, to abuse, etc.: "As a politician, Thomas was always ready to assail his opponent with slander."
3. To undertake a task with the purpose of mastering it: "Joanne assailed her university studies with new determination."
4. To impinge upon; to make an impact on; to beset: "The minds of the audience were assailed by all of the conflicting arguments presented by the speakers."