They would need to be able to live without breathing anything, for sure.
Their muscles and bones would have to be exempt from atrophy, because you aren't using your bones much in space so they would tend to thin out. If their muscles never atrophy, then they probably aren't growing much muscle regularly either, so they must have some mechanism for movement other than human-style sinews which contract. Maybe they move by means of some kind of magnetism (the way electric 3-phase motors and solenoids do). Or maybe they move by filling pouches with fluid to expand them (kindof like pneumatics, but with pouches). Or maybe they move by popping little round nodes to convex or concave, (like a venus fly trap). Or maybe they move by altering their crystal structure to produce little pieces that stick out and then come back in on various parts of their body (I don't know of anything that does that).
They need to get their energy from somewhere, so I'm thinking starlight is abundant enough in space that they can use that. But absorbing light means that you aren't getting very much energy very often (especially while you're on a planet with a dense atmosphere). So they need to have the ability to store a lot of energy long term, only expending what they use. So maybe on a planet with an atmosphere which doesn't allow any sunlight through, they can only be on the planet for a few weeks before they start running out of energy.
But if your creatures are organic then it's likely that they grow physically during their lives. Hydrogen is abundant in space, so a good race that eats should be able to eat just about anything with hydrogen in it, and then internally transmute that into helium, and then carbon. This implies that they have nuclear fusion reactions going on in their bellies, so they will need to do that in very small amounts at a time to maintain their physical existence safely. They'll have very warm internal body temperatures during whatever phase in their life they want to grow (maybe they grow as long as they're alive, maybe they choose to grow whenever they have time for it). Since they need to be able to handle very cold external temperatures, I'm thinking they must have a well insulating exoskeleton, and since they are using hydrogen to grow it means they'll shed their exoskeleton on a regular basis as they grow.
Standing upright on two legs is good for a being which is well adapted to one single planet with a very specific gravity. A race which is able to travel to any other planet, and handle the wide variety of gravitational pulls on those planets, would have numerous short legs, or no legs. Short legs are harder to break, and easier to push yourself up on, and if you have more than four of them then you can stand on some while you move others. The race would need a flexible body, too, to handle various terrains. So with the exoskeleton, maybe a segmented body like a millipede (but it doesn't have to be long like a millipede). It doesn't make much sense for a race adapted to the maximum possible planets to have wings, because they depend on gasses being around to push against.
The size of the race is effectively arbitrary; no matter how big you make them, there will always be a bigger race out there somewhere. If you make them too small, though, then it could get hard to manage production of energy eventually. A small race has some advantages related to their ability to keep food for a long time, etc.. They could survive for a long time on a small cash of food.
A hardcore surviving species should have tons of kids in one gestation cycle and be ok with many of them dying, but expect each one of them to share its food with the pack (think cockroaches). However, since this race is adapted to minimizing energy use and storing it long term, it might make sense for them to have few babies and work hard storing up energy to produce each one, like people do. You'll have to decide if you want them to gestate their babies internally, or externally in eggs -- and that might depend on how they get around space and their social structure. Maybe they shoot their eggs into space at random and the eggs hatch and colonize nearby planets, or maybe they keep their babies close and teach them the culture of their parents.
Anyway, this post is getting long. I hope it helps!