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Relativistic high-order harmonics from a few-cycle laser driven plasma surface is a very promising source of anintense and isolated attosecond light pulse. The laser to harmonics conversion efficiency and the “purity” ofan isolated attosecond light pulse are generally determined by a combination of interaction parameters, suchas laser intensities, incidence angles, pulse durations, carrier-envelope phases and plasma scale lengths. Wehad already previously investigated the effect of a three-parameter combination of the laser pulse duration,the carrier-envelope phase and the plasma scale length. To complement our previous work, the parametricdependence of the other two three-parameter combinations: the carrier-envelope phase, the plasma scale length,either combined with the laser intensity or the incidence angle, were systematically investigated through onedimensional particle-in-cell simulations. We found that, although the impact of parameter combinations onattosecond pulse generations is generally complicated, there exist however an optimal plasma scale length and anoptimal incidence angle to efficiently generate high-order harmonics and intense attosecond light pulses. Whenother parameters are fixed, a moderately intense relativistic laser is more advantageous to realize an isolatedattosecond light pulse in a broad controlling parameters range. And a larger incidence angle favors a higherisolation degree as well as a broader range of controlling parameters towards the generation of intense isolatedattosecond light pulses. In order to interpret these simulation results, we have modeled the correspondingrelativistic electron dynamics, using which the underlying physics are discussed.