Social media has become an everyday means of interaction and information sharing on the Internet. However, posts on social networks are often aggressive and toxic, especially when the topic is controversial or politically charged. Radicalization, extreme speech, and in particular online misogyny against women in the public eye have become alarmingly negative features of online discussions. The present study proposes a methodological approach to contribute to ongoing discussions about the multiple ways in which women, their experiences, and their choices are attacked in polarized social media responses. Based on a review of theories on and detection methods for misogyny, we present a classification scheme that incorporates eleven different explicit as well as implicit layers of online misogyny. We also apply our classes to a case study related to online aggression against Amber Heard in the context of her allegations of domestic violence against Johnny Depp. We finally evaluate the reliability of Google's Perspective API -- a standard for detecting toxic language -- for determining gender discrimination as toxicity. We show that a large part of online misogyny, especially when verbalized without expletive terms but instead more implicitly is not captured automatically.