Soft materials with mechanical adaptability have substantial potential for various applications in tissue engineering. Gaining a deep understanding of the structural evolution and adaptation dynamics of soft materials subjected to cyclic stretching gives insight into developing mechanically adaptive materials. Here, we investigate the effect of hierarchy structure on the mechanical adaptation of self-healing hydrogels under cyclic stretching training. A polyampholyte hydrogel, composed of hierarchical structures including ionic bonds, transient and permanent polymer networks, and bicontinuous hard/soft-phase networks, is adopted as a model. Conditions for effective training, mild overtraining, and fatal overtraining are demonstrated in soft materials. We further reveal that mesoscale hard/soft-phase networks dominate the long-term memory effect of training and play a crucial role in the asymmetric dynamics of compliance changes and the symmetric dynamics of hydrogel shape evolution. Our findings provide insights into the design of hierarchical structures for adaptive soft materials.