Breathwork is a term for an understudied school of practices that involve the intentional modulation of respiration to induce an altered state of consciousness (ASC). We map here the neural dynamics of mental content during breathwork, using a neurophenomenological approach by combining Temporal Experience Tracing, a quantitative phenomenological methodology that preserves the temporal dynamics of subjective experience, with low-density portable EEG devices for every session. Fourteen novice participants completed a series of up to 28 breathwork sessions - of 20, 40 or 60 minutes - in 28 days, yielding a neurophenomenological dataset of 301 breathwork sessions. Using hypothesis-driven and data-driven approaches, we found that positive ‘psychedelic-like’ subjective experiences that occurred within the breathwork sessions were associated with increased neural Lempel-Ziv complexity. Further, exploratory analyses showed that the aperiodic exponent of the power spectral density (PSD) - but not oscillatory alpha power - was also associated with these psychedelic-like phenomenological substates. We demonstrate the strength of this neurophenomenological framework, maximising the concurrent data acquisition of brain activity and phenomenological dynamics in multiple experiential dimensions. Non-linear aspects of brain dynamics, like complexity and the aperiodic exponent of the PSD, neurally map both a data-driven complex composite of positive experiences, and hypothesis-driven aspects of psychedelic-like experience states such as high bliss.