Learning fine-grained embeddings from coarse labels is a challenging task due to limited label granularity supervision, i.e., lacking the detailed distinctions required for fine-grained tasks. The task becomes even more demanding when attempting few-shot fine-grained recognition, which holds practical significance in various applications. To address these challenges, we propose a novel method that embeds visual embeddings into a hyperbolic space and enhances their discriminative ability with a hierarchical cosine margins manner. Specifically, the hyperbolic space offers distinct advantages, including the ability to capture hierarchical relationships and increased expressive power, which favors modeling fine-grained objects. Based on the hyperbolic space, we further enforce relatively large/small similarity margins between coarse/fine classes, respectively, yielding the so-called hierarchical cosine margins manner. While enforcing similarity margins in the regular Euclidean space has become popular for deep embedding learning, applying it to the hyperbolic space is non-trivial and validating the benefit for coarse-to-fine generalization is valuable. Extensive experiments conducted on five benchmark datasets showcase the effectiveness of our proposed method, yielding state-of-the-art results surpassing competing methods.