Specific heat measurements of Eu0.9Ho0.1Mo6S8 were performed using an ac calorimetry technique under the extreme conditions of low temperature, high magnetic field, and hydrostatic pressure. The title compound is a Chevrel phase material, which is paramagnetic at ambient pressure, becomes superconducting for pressures above 7 kbar, and has a reentrant upper critical field [dHc2(T)/dT>0, as T --> 0 K]. Evidence that this material also has a high field-induced superconducting phase at low temperatures (H > 5 T, T < 1 K) was previously reported. The present ac calorimetry study carried out for 0.15 less-than-or-equal-to T less-than-equal-to 6 K, 0 less-than-or-equal-to H less-than-or-equal-to 20 T, and P congruent-to 8 kbar, shows a sharp superconducting transition for T < 1 K in the specific heat, which broadens at higher fields and temperatures. The results are analyzed to obtain a reentrant phase in agreement with previous transport work, but direct evidence for the high field-induced phase was not found. The mechanism for the field and temperature dependence of the superconductivity of Eu0.9Ho0.1Mo6S8 is discussed.