The 21-cm absorption feature reported by the EDGES collaboration is several times stronger than that predicted by traditional astrophysical models. If genuine, a deeper absorption may lead to stronger fluctuations on the 21-cm signal on degree scales (up to 1~Kelvin in rms), allowing these fluctuations to be detectable in nearly 50~times shorter integration times compared to previous predictions. We commenced the AARTFAAC Cosmic Explorer (ACE) program, that employs the AARTFAAC wide-field imager, to measure or set limits on the power spectrum of the 21-cm fluctuations in the redshift range $z = 17.9-18.6$ ($Delta u = 72.36-75.09$~MHz) corresponding to the deep part of the EDGES absorption feature. Here, we present first results from two LST bins: 23.5-23.75h and 23.5-23.75h, each with 2~h of data, recorded in `semi drift-scan mode. We demonstrate the application of the new ACE data-processing pipeline (adapted from the LOFAR-EoR pipeline) on the AARTFAAC data. We observe that noise estimates from the channel and time-differenced Stokes~$V$ visibilities agree with each other. After 2~h of integration and subtraction of bright foregrounds, we obtain $2sigma$ upper limits on the 21-cm power spectrum of $Delta_{21}^2 < (8139~textrm{mK})^2$ and $Delta_{21}^2 < (8549~textrm{mK})^2$ at $k = 0.144~h,textrm{cMpc}^{-1}$ for the two LST bins. Incoherently averaging the noise bias-corrected power spectra for the two LST bins yields an upper limit of $Delta_{21}^2 < (7388~textrm{mK})^2$ at $k = 0.144~h,textrm{cMpc}^{-1}$. These are the deepest upper limits thus far at these redshifts.
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