Transformer-based models have unlocked a plethora of powerful intelligent applications at the edge, such as voice assistant in smart home. Traditional deployment approaches offload the inference workloads to the remote cloud server, which would induce substantial pressure on the backbone network as well as raise users' privacy concerns. To address that, in-situ inference has been recently recognized for edge intelligence, but it still confronts significant challenges stemming from the conflict between intensive workloads and limited on-device computing resources. In this paper, we leverage our observation that many edge environments usually comprise a rich set of accompanying trusted edge devices with idle resources and propose Galaxy, a collaborative edge AI system that breaks the resource walls across heterogeneous edge devices for efficient Transformer inference acceleration. Galaxy introduces a novel hybrid model parallelism to orchestrate collaborative inference, along with a heterogeneity-aware parallelism planning for fully exploiting the resource potential. Furthermore, Galaxy devises a tile-based fine-grained overlapping of communication and computation to mitigate the impact of tensor synchronizations on inference latency under bandwidth-constrained edge environments. Extensive evaluation based on prototype implementation demonstrates that Galaxy remarkably outperforms state-of-the-art approaches under various edge environment setups, achieving up to 2.5x end-to-end latency reduction.