We demonstrate generation of pulses with up to 4 μJ energy at 1 MHz repetition rate through nonlinear chirped-pulse amplification in an entirely fiber-integrated amplifier, seeded by a fiber oscillator. The peak power and the estimated nonlinear phase shift of the amplified pulses are as much as 57 kW and 22π, respectively. The shortest compressed pulse duration of 140 fs is obtained for 3.1 μJ of uncompressed amplifier output energy at 18 π of nonlinear phase shift. At 4 μJ of energy, the nonlinear phase shift is 22 π and compression leads to 170-fs-long pulses. Numerical simulations are utilized to model the experiments and identify the limitations. Amplification is ultimately limited by the onset of Raman amplification of the longer edge of the spectrum with an uncompressible phase profile.