We present a spectroscopic study of the most massive stars in the young (4 Myr old) stellar cluster LH 95 in the Large Magellanic Cloud. This analysis allows us to complete the census of the stellar population of the system, previously investigated by us down to 0.4 M⊙ with deep Hubble Space Telescope Advanced Camera for Surveys photometry. We perform spectral classification of the five stars in our sample, based on high-resolution optical spectroscopy obtained with the 2.2-m MPG/ESO Fibre-fed Extended Range Optical Spectrograph. We use complementary ground-based photometry, previously performed by us, to place these stars in the Hertzsprung–Russell diagram. We derive their masses and ages by interpolation from evolutionary models. The average ages and age spread of the most massive stars are found to be in general comparable with those previously derived for the cluster from its low-mass pre-main-sequence stars. We use the masses of the five sample stars to extend to the high-mass end the stellar initial mass function of LH 95 previously established by us. We find that the initial mass function follows a Salpeter relation down to the intermediate-mass regime at 2 M⊙. The second most massive star in LH 95 shows broad Balmer line emission and infrared excess, which are compatible with a classical Be star. The existence of such a star in the system adds a constrain to the age of the cluster, which is well covered by our age and age spread determinations. The most massive star, a 60–70 M⊙ O2 giant, is found to be younger (<1 Myr) than the rest of the population. Its mass in relation to the total mass of the system does not follow the empirical relation of the maximum stellar mass versus the hosting cluster mass, making LH 95 an exception to the average trend.