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Virtualized network slicing allows a multitude of logical networks to be created on a common substrate infrastructure to support diverse services. A virtualized network slice is a logical combination of multiple virtual network functions, which run on virtual machines (VMs) as software applications by virtualization techniques. As the performance of network slices hinges on the normal running of VMs, detecting and analyzing anomalies in VMs are critical. Based on the three-tier management framework of virtualized network slicing, we first develop a federated learning (FL) based three-tier distributed VM anomaly detection framework, which enables distributed network slice managers to collaboratively train a global VM anomaly detection model while keeping metrics data locally. The high-dimensional, imbalanced, and distributed data features in virtualized network slicing scenarios invalidate the existing anomaly detection models. Considering the powerful ability of generative adversarial network (GAN) in capturing the distribution from complex data, we design a new multi-discriminator Bidirectional Wasserstein GAN with Gradient Penalty (BiWGAN-GP) model to learn the normal data distribution from high-dimensional resource metrics datasets that are spread on multiple VM monitors. The multi-discriminator BiWGAN-GP model can be trained over distributed data sources, which avoids high communication and computation overhead caused by the centralized collection and processing of local data. We define an anomaly score as the discriminant criterion to quantify the deviation of new metrics data from the learned normal distribution to detect abnormal behaviors arising in VMs. The efficiency and effectiveness of the proposed collaborative anomaly detection algorithm are validated through extensive experimental evaluation on a real-world dataset.