I have soloed all content in this game outside of the things teammates are required to start (incarnate trials, MSR, Hami, etc.) with my Ice Blast/Cold Domination/Ice Mastery Corruptor. I have every souvenir, collected nearly ever badge (outside incarnate content and Master of stuff), and played the same character for over five years now. This anecdotal evidence implies any other Archetype and powerset combination could also do so under the same constraints.