We apply a Wilsonian renormalization group approach to the continuum limit of the attractive t − t′ Hubbard model, taken when the Fermi level is at the Van Hove singularity of the density of states. We determine the leading instabilities by computing the different response functions up to t′ = 0.5 t. The phase diagram shows a large boundary between superconducting and charge-density-wave phases, that merge in a triple point with a phase separation instability. The latter is realized down to very low coupling constant, as the Fermi sea degenerates towards a pair of straight lines near t′ = 0.5 t.