The production of a Higgs boson in association with a top-antitop quark pair \( \left(t\overline{t}H\right) \) holds significant importance in directly probing the top-quark Yukawa coupling, which is related to various fundamental questions in high energy physics. This paper focuses on the calculation of two-loop amplitudes for \( t\overline{t}H \) production at hadron colliders in the high-energy boosted limit. The calculation employs our recently developed mass-factorization formula. To validate the accuracy of our approximate methods, we compare our results for the one-loop amplitudes and the two-loop infrared poles with the exact calculations. We then provide predictions for the finite parts of the two-loop amplitudes. By combining the contributions from real emissions, our results can be utilized to compute the next-to-next-to-leading order differential cross sections for \( t\overline{t}H \) production in the high-energy boosted limit.
