We present DreamBeast, a novel method based on score distillation sampling (SDS) for generating fantastical 3D animal assets composed of distinct parts. Existing SDS methods often struggle with this generation task due to a limited understanding of part-level semantics in text-to-image diffusion models. While recent diffusion models, such as Stable Diffusion 3, demonstrate a better part-level understanding, they are prohibitively slow and exhibit other common problems associated with single-view diffusion models. DreamBeast overcomes this limitation through a novel part-aware knowledge transfer mechanism. For each generated asset, we efficiently extract part-level knowledge from the Stable Diffusion 3 model into a 3D Part-Affinity implicit representation. This enables us to instantly generate Part-Affinity maps from arbitrary camera views, which we then use to modulate the guidance of a multi-view diffusion model during SDS to create 3D assets of fantastical animals. DreamBeast significantly enhances the quality of generated 3D creatures with user-specified part compositions while reducing computational overhead, as demonstrated by extensive quantitative and qualitative evaluations.