This paper studies the problem of text-attributed hypergraph self-supervised representation learning, which aims to generate discriminative representations of hypergraphs without any annotations for downstream tasks. However, real-world hypergraphs could contain incomplete signals, which could deteriorate the representation learning procedure, especially under label scarcity. Towards this end, we introduce a new perspective that leverages large language models to enhance hypergraph self-supervised learning and propose a novel data-centric approach named Hybrid Hypergraph Enhancement with LLM-based Agents (HEAL). The core of our HEAL is to generate informative nodes and hyperedges through multi-round interaction with LLM-based agents. In particular, we first retrieve similar samples for each node to facilitate the node expansion agent for different views. To generate challenging samples, we measure the gradients for each augmented view and select the most informative one using an evaluation agent. From the structural view, we adopt a topology refinement agent to incorporate new hyperedges for the recovery of missing structural signals. The enhanced hypergraphs would be incorporated into a self-supervised learning framework for discriminative representations. Extensive experiments on several datasets validate the effectiveness of our HEAL in comparison with extensive baselines.