This is the 14432nd most frequent Russian word.
отчаяния
Despair.
Here, the word 'отчаяния' is used as a noun in the genitive case to indicate the cause of the state he is experiencing.
Он погрузился в глубокие чувства отчаяния.
He sank into deep feelings of despair.
In this sentence, 'отчаяния' is used to describe the characteristics or nature of the cry.
Её крик был выражением отчаяния.
Her cry was an expression of despair.
Here, 'отчаяния' is employed to describe the motivational state influencing his actions.