We propose an adaptive master-slave coupling scheme to achieve explosive synchronization (ES) in a targeted (slave) layer of a multilayer network of Sakaguchi-Kuramoto (SK) oscillators. The natural frequencies of the oscillators in the networks are drawn from Lorentzian distribution of zero mean. In the absence of inter-layer coupling, the dynamics of the master layer is governed by SK model with local adaptive coupling and the layer exhibits ES for wide ranges of the parameters. On the other hand, the targeted layer also consists of SK model but does not exhibit ES. Under the proposed coupling scheme, a feedback is sent to a percentage of nodes in the slave layer in the form of local order parameters of the master layer to achieve ES in the slave layer. Our numerical experiment shows that the proposed coupling scheme can induce ES in the slave layer even when a very small percentage of nodes receive feedback from the master layer. The area of the hysteresis region in the slaved layer is found to be steadily increasing with the increase in the percentage of feedback receiving nodes of the slave layer. In the ES regime, an amplification in the hysteresis width in the slave layer is also achieved by tuning a parameter in the adaptive coupling function of the master layer. The scheme proposed here is found to be robust and can induce ES in a variety of networks in the slave layer.