The anger in this soliloquy is directed mostly towards his mother, in frustration over her marriage to his uncle. Hamlet's father had died just two months earlier, and already Gertrude had remarried, to Hamlet's uncle Claudius. This occurrence is mortifying to Hamlet, incredibly depressing, and incenses him. He feels that his mother is weak, inconstant, violating his father's honor and memory, and he is angry about it. He doesn't understand how his mother could
"hang on [his father] as if increase of appetite had grown by what it fed on: and yet, within a month"
had strayed from her love and married another. She used to adore Hamlet's father, hang on him, worship and adore him. And yet, it seems like it was all a ruse, because she so quickly tranferred her affections to another.
As the son of the dead king, Hamlet is furious that his mother would dishonor his father. Her actions seem to spit on the memory of his father, tarnish his majestic reputation as a powerful king, and say a whole lot of negative things about the faithfulness of women in general. Her actions make him declare with disgust, "frailty, they name is woman!" and turn against his mother. Later, he lashes out in rage against her, and other women in his life. I hope that those thoughts helped; good luck!
In my opinion, His anger in this line is aimed at Claudius and the Queen, but also at Denmark in general, at the world and at himself.
After this line he goes on to say; "that the Everlasting had not fixed His canon 'gainst self slaughter. O God, God, How weary, stale, flat and unprofitable Seem to me all the uses of this world!"
He hints again at suicide, proving my point that he is obviously angry at himself or at his own life to be as melancholic to take it away. He blaimes God, so his anger is also directed there. And describes bitterly the world.
He goes on to say say how "things rank and gross in nature Posses it merely", which could be a reference to Denmark's political neglect and corruption, therefore displaying his anger at Claudius. He describes how the people who live or "posses" Denmark are "gross", This could reference Claudius and Gertrude.
He then vents his anger at his mothers speedy re-marriage.
But those are just my opinions :) x