Entering the tun involves retracting the legs, contracting the body, losing most body water and shutting down measurable metabolism. Desiccation-tolerant species accumulate protective molecules, including trehalose in some lineages and, notably, a set of intrinsically disordered proteins that vitrify as water leaves and hold cellular structures in place.
The genome of Ramazzottius varieornatus revealed one such protein, Dsup, which associates with DNA and reduces damage from radiation and reactive oxygen species. Introduced into cultured human cells, it reduced X-ray-induced DNA damage, which is why the animal appears in radiation-biology work.
The headline claims need trimming. Tardigrades exposed to open space on a 2007 orbital experiment survived vacuum and solar ultraviolet in the dried state, and some survived long enough to reproduce afterwards, but survival was not universal and this is tolerance, not thriving. A crashed lunar lander in 2019 carried dried tardigrades; there is no evidence any survived the impact, and none could grow or reproduce on the Moon. How well individual species tolerate any given stress varies widely and is unevenly measured.