Well, clearly one of the biggest examples of irony in this scene emerges from the way that Cassius misconstrued what happened when he sent Titinius to see what was happening. Cassius thought that Titinius had been captured and that the shouts of joy were from the opposition soldiers at having captured him, whereas in fact it was the shouts of joy from Brutus's soldiers at being victorious. Brutus had given Titinius a victory garland to give to Cassius, but ironically, the shouts of joy that heralded Cassius's victory resulted in his death.
Secondly, I would say that it is ironic how reference is made yet again to how Julius Caesar's might and power outlives his mortal body. When Brutus discovers what has happened and how Cassius has died, he attributes the disaster immediately to the power of Caesar:
O Julius Caesar, thou art mighty yet!
Thy spirit walks abroad, and turns our swords
In our own proper entrails.
Ironically, Caesar only seems to have been made more powerful through his assassination, whereas obviously the conspirators thought that his death would be the end of him.
Lastly, I would say by far the keenest irony lies in the character of Cassius. Throughout the play, he shows himself to be an incredibly shrewd reader of situations and characters. He knows just how to manipulate Brutus to get him to join the conspirators. He recognises the danger of Antony and recommends he be killed, and then he also advises Brutus to not let him address the crowd at Caesar's funeral. However, in this one fatal incident, he reads the situation badly, and dies as a result.