The yielding behavior of silica nanoparticles partitioned at an air aqueous interface is reported. Linear viscoelasticity of the particle-laden interface can be retrieved via a time-dependent and electrolyte-dependent superposition, and the applicability of the "soft glassy rheology" (SGR) model is confirmed With increasing electrolyte concentration (phi(elect)) in the aqueous subphase, a nonergodic state is achieved with particle dynamics arrested first from attraction induced bonding bridges and then from the cage effect of particle jamming, manifesting in a two-step yielding process under large amplitude oscillation strain (LAOS). The Lissajous curves disclose a shear-induced in-cage particle redisplacement within oscillation cycles between the two yielding steps, exhibiting a "strain softening" transitioning to "strain stiffening" as the interparticle attraction increases. By varying phi(elect) and the particle spreading concentration, phi(SiO2), a variety of phase transitions from fluid- to gel- and glass-like can be unified to construct a state diagram mapping the yielding behaviors from one-step to two-step before finally exhibiting one-step yielding at high phi(elect) and phi(SiO2).