This paper investigates the behavior of P(NIPAM-co-AAc)@PTFMA core-shell microgels at the decane/water interface. The microgels were deposited at the interface to form a monolayer film, and the film's compression behavior was measured using Langmuir trough. Typical compression isotherm embodies four regimes, weak interaction between microgels in regime I, viscoelastic deformation in regime II, elastic deformation of microgels with thin shell while still viscoelastic deformation with thick shell in regime III. Minor desorption of microgels takes place in regime III and massive in regime IV. The critical interfacial pressure for desorption of microgels is identified in the range of 43-45 mN/m, independent of the shell thickness. It shows that the deformability of the surrounding part rather than the mean deformation of the microgels dominates their stability at the interface. These results illustrate the behavior of microgels at the interface under loading, and deepen the understanding of the stability of microgel-stabilized emulsion.