Feature-based physical layer authentication (PLA) schemes, using position-specific channel characteristics as identifying features, can provide lightweight protection against impersonation attacks in overhead-limited applications like e.g., mission-critical and low-latency scenarios. However, with PLA-aware attack strategies, an attacker can maximize the probability of successfully impersonating the legitimate devices. In this paper, we provide worst-case detection performance bounds under such strategies for a distributed PLA scheme that is based on the channel-state information (CSI) observed at multiple distributed remote radio-heads. This distributed setup exploits the multiple-channel diversity for enhanced detection performance and mimics distributed antenna architectures considered for 4G and 5G radio access networks. We consider (i) a power manipulation attack, in which a single-antenna attacker adopts optimal transmit power and phase; and (ii) an optimal spatial position attack. Interestingly, our results show that the attacker can achieve close-to-optimal success probability with only statistical CSI, which significantly strengthens the relevance of our results for practical scenarios. Furthermore, our results show that, by distributing antennas to multiple radio-heads, the worst-case missed detection probability can be reduced by 4 orders of magnitude without increasing the total number of antennas, illustrating the superiority of distributed PLA over a co-located antenna setup.