We present the re-calibrated and re-imaged fits-cubes of the first set of data from the DEATHSTAR project (DEtermining Accurate mass-loss rates for THermally pulsing AGB STARs, www.astro.uu.se/deathstar). Forty-two southern AGB stars, 21 carbon stars and 21 M-type stars, were mapped in Bands 6 and 7 with the Atacama Compact Array (ACA). Source selection, detected line emission, data calibration procedures etc. are described in detail in the paper. The beams are typically 4-8 and 3-5-arcseconds in Band 6 and 7, respectively. The rms noise level reached is typically 50-70 and 100-150mJy/beam in Band 6 and 7, respectively. More exact beam sizes and rms values for each source are listed in the paper together with tentative line detections.