Starting with Carnot engine, the ideal efficiency of a heat engine has been associated with quasi-static transformations and vanishingly small output power. Here, we exactly calculate the thermodynamic properties of a isothermal heat engine, in which the working medium is a periodically driven underdamped harmonic oscillator, focusing instead on the opposite, anti-adiabatic limit, where the period of a cycle is the fastest time scale in the problem. We show that in that limit it is possible to approach the ideal energy conversion efficiency $eta=1$, with finite output power and vanishingly small relative power fluctuations. The simultaneous realization of all the three desiderata of a heat engine is possible thanks to the breaking of time-reversal symmetry. We also show that non-Markovian dynamics can further improve the power-efficiency trade-off.
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