Several recent works have been dedicated to unsupervised reinforcement learning in a single environment, in which a policy is first pre-trained with unsupervised interactions, and then fine-tuned towards the optimal policy for several downstream supervised tasks defined over the same environment. Along this line, we address the problem of unsupervised reinforcement learning in a class of multiple environments, in which the policy is pre-trained with interactions from the whole class, and then fine-tuned for several tasks in any environment of the class. Notably, the problem is inherently multi-objective as we can trade off the pre-training objective between environments in many ways. In this work, we foster an exploration strategy that is sensitive to the most adverse cases within the class. Hence, we cast the exploration problem as the maximization of the mean of a critical percentile of the state visitation entropy induced by the exploration strategy over the class of environments. Then, we present a policy gradient algorithm, alphaMEPOL, to optimize the introduced objective through mediated interactions with the class. Finally, we empirically demonstrate the ability of the algorithm in learning to explore challenging classes of continuous environments and we show that reinforcement learning greatly benefits from the pre-trained exploration strategy w.r.t. learning from scratch.