The Planck All-Sky Survey to Analyze Gravitationally-lensed Extreme Starbursts project aims to identify a population of extremely luminous galaxies using the Planck all-sky survey and to explore the nature of their gas fuelling, induced starburst, and the resulting feedback that shape their evolution. Here, we report the identification of 22 high-redshift luminous dusty star-forming galaxies (DSFGs) at z = 1.1-3.3 drawn from a candidate list constructed using the Planck Catalogue of Compact Sources and Wide-field Infrared Survey Explorer all-sky survey. They are confirmed through follow-up dust continuum imaging and CO spectroscopy using AzTEC and the Redshift Search Receiver on the Large Millimeter Telescope Alfonso Serrano. Their apparent infrared luminosities span (0.1-3.1) × 1014 Lpdbl (median of 1.2 × 1014 Lpdbl), making them some of the most luminous galaxies found so far. They are also some of the rarest objects in the sky with a source density of 0.01 deg-2. Our Atacama Large Millimeter/submillimeter Array 1.1 mm continuum observations with θ ≈ 0.4 arcsec resolution show clear ring or arc morphologies characteristic of strong lensing. Their lensing-corrected luminosity of LIR - 1013 Lpdbl (star-formation rate - 103 Mpdbl yr-1) indicates that they are the magnified versions of the most intrinsically luminous DSFGs found at these redshifts. Our spectral energy distribution analysis finds little detectable active galactic nucleus (AGN) activity despite their enormous luminosity, and any AGN activity present must be extremely heavily obscured.