We consider an agent acting in a complex environment modeled through a multi-tiered specification, in which each tier adds nondeterminism in the environment response to the agent actions. In this setting, we devise an effective approach to best-effort synthesis, i.e., synthesizing agent strategies that win against a maximal set of possible environment responses in each tier. We do this in a setting where both the multi-tier environment and agent goal are specified in the linear temporal logic on finite traces (LTLf). While theoretical solution techniques based on automata on infinite trees have been developed previously, we completely side-step them here and focus on a DFA-based game-theoretic technique, which can be effectively implemented symbolically. Specifically, we present a provably correct algorithm that is based on solving separately DFA-based games for each tier and then combining the obtained solutions on-the-fly. This algorithm is linear, as opposed to being exponential, in the number of tiers and thus, it can graciously handle multi-tier environments formed of several tiers.