We study a sample composed of 28 of the brightest stars in the Arches cluster. We analyze K-band spectra obtained with the integral field spectrograph SINFONI on the VLT. Atmosphere models computed with the code CMFGEN are used to derive the effective temperatures, luminosities, stellar abundances, mass loss rates and wind terminal velocities. We find that the stars in our sample are either H-rich WN7-9 stars (WN7-9h) or O supergiants, two being classified as OIf+. All stars are 2-4 Myr old. There is marginal evidence for a younger age among the most massive stars. The WN7-9h stars reach luminosities as large as 2 x 1e6 Lsun, consistent with initial masses of ~ 120 Msun. They are still quite H-rich, but show both N enhancement and C depletion. They are thus identified as core H-burning objects showing products of the CNO equilibrium at their surface. Their progenitors are most likely supergiants of spectral types earlier than O4-6 and initial masses > 60 Msun. Their winds follow a well defined modified wind momentum - luminosity relation (WLR): this is a strong indication that they are radiatively driven. Stellar abundances tend to favor a slightly super solar metallicity, at least for the lightest metals. We note however that the evolutionary models seem to under-predict the degree of N enrichment.