Complex sentence: After witnessing Izumiko's ability to identify Takayanagi's spirit agents she realizes that Izumiko and Miyuki might be more powerful than she thought and decides to try to recruit Izumiko and attacks Miyuki to reveal his true strength.
Split into simpler sentences: After witnessing Izumiko's ability to identify Takayanagi's spirit agents, she realizes that Izumiko and Miyuki might be more powerful than she thought. She decides to try and recruit Izumiko, and attacks Miyuki to reveal his true strength.