Equiano responds with shock and horror to the conditions he describes aboard the slave ship on the Middle Passage. Equiano is struck by the claustrophobic conditions below decks, and describes in lurid detail the smells of sweat and human waste as well as the screams and moans of slaves confined in these awful conditions: 

...the filth of the necessary tubs, into which the children often fell, and were almost suffocated. The shrieks of the women, and the groans of the dying, rendered the whole a scene of horror almost inconceivable.

Equiano is so ill that he is kept above deck for a large portion of the journey, in an effort to save his life (and the slavers' investment in his survival for sale). It is unclear, however, whether Equiano intentionally exaggerated his injury in order to stay above decks, which historians have found to be common practice among slaves, and a means of exercising agency to influence their own situations. Equiano describes the cruelty of the white crew, many of which, he notes, were treated barbarously by the ship's officers as well. Overall, aside from his visceral reaction to the horrors of the Middle Passage, he is struck by the evil and the greed of the slavers, who he, in a passage typical of slave narratives produced for the abolition movement, describes as hypocritical, especially as they separated children from their parents at the infamous slave auctions:

O, ye nominal Christians! might not an African ask you, learned you this from your God, who says unto you, Do unto all men as you would men should do unto you? Is it not enough that we are torn from our country and friends to toil for your luxury and lust of gain? Must every tender feeling be likewise sacrificed to your avarice?

How did Equiano respond to challenges during the Middle Passage?

The original question had to be edited down.  I think that Equiano clearly makes the case that mental fortitude and toughness were the necessary requirements to endure the conditions of the Middle Passage.  It is through his detail that the savagery of slave traders becomes evident. The traditional notion of the slave being a savage that required controlled is flipped here.  It is the slaveowner and slave trader whose savage condition is evident, as it would only be someone this savage that could wish to inflict so much suffering on other human beings.  Equiano makes it clear that his ability to endure and struggle through these difficult times as well as the challenging conditions of slavery are what enabled him to live.  At the same time, his narrative makes clear how slaves can envision and construct a better life for themselves once free from the slave condition.  It is in this call where Equiano's narrative becomes so compelling.  It forces the change that the abolitionist movement had been so insistent in demanding.  Equiano makes clear that the mental toughness required to survive the harsh conditions of the Middle Passage and, of slavery, in general justify the need for slavery to be abolished and for former slaves to reclaim their own lives as human beings.