By the end of Act 1, Don John has made the resolution to try and double-cross Claudio, thereby double-crossing his brother, Prince Don Pedro. Don John is Don Pedro's illegitimate brother; however, due to his illegitimacy, Don John feels like an outcast. He is also very gloomy by nature, as we see in his lines, "I cannot hide what I am: I must be sad when I have cause, and smile at no man's jests" (I.iii.10-11).
He has also become very jealous of Claudio whom the prince is treating as his right-hand man. Don John would prefer to be given more power and treated with more importance by the prince. Hence, when Don John learns that Claudio wishes to marry Hero and that Don Pedro has promised to court Hero for him and then give her to Claudio, Don John decides this could be a good way for him to make "mischief" (37). He further declares that he would love it if he could find a way to cross Claudio, as we see in his lines, "If I can cross him any way, I bless myself every way" (56-57).
Hence, by the end of the first act, we know that Don John has resolved to try and sabotage Claudio's intended marriage to Hero although at this point we don't know yet what his exact plans are.