The Tek Dedicated Storage Box is unlocked upon defeating

Dragon(Beta): The Island, Ragnarok

Manticore(Beta): Scorched Earth, Ragnarok

Rockwell(Beta): Aberration

Crystal Wyvern Queen(Beta): Crystal Isles

Desert Titan: Extinction

Corrupted Master Controller(Gamma): Genesis Part 1

Dinopithecus King(Beta): Lost Island

Rockwell Prime(Gamma): Genesis Part 2