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We report direct full-field magneto-optical observations of Barkhausen avalanches in Co polycrystalline thin films at criticality. We provide experimental evidence for the validity of a phenomenological model of the Barkhausen avalanche originally proposed by Cizeau, Zapperi, Durin, and Stanley [Phys. Rev. Lett. 79, 4669 (1997)], where the model describes a -type flexible domain wall deformed by a localized defect with consideration of long-range dipolar interaction. The Barkhausen jump areas show a power-law scaling distribution with critical exponent for all the samples having different thickness from 5 to 50 nm, which is in accord with the two-dimensional prediction of the model.