In a play defined by vengeance and betrayal, Gertrude is unique in that in many ways she actually has no enemies. None of the play's major characters are plotting to harm Gertrude. Claudius wants her as his wife, and so his treacherous plots against the older Hamlet and later against her son do not include her. Additionally, even though the older Hamlet's ghost shows distaste for Gertrude's actions, he makes a point to stress that his son should not harm her.
That said, there are many ways in which she certainly does have enemies. While he never plots to kill her, the younger Hamlet still views her as playing a role in his father's betrayal. He calls her lustful and frail. He plots to unravel her marriage by killing her husband. In this sense, her son could be seen as a less direct form of enemy. From another perspective, Claudius could be considered her enemy. She shows signs of affection for her new husband, but she does not seem to know that he has murdered her last husband. By pulling her unknowingly into his treachery and starting a deadly conflict with her son, Claudius does her great harm. In this sense, he is her enemy, even if she does not realize it.
From a very simple perspective the Norwegian armies plotting to attack Denmark could be considered her enemies as well.