Challenges is a side tasks in game. They not required to complete storyline, but can give you extra xp and fun. But they required to finish game on 100% and to achieve "Inconceivable!" achievement.
I wrote this guide because items, required to complete challenge, is hard to find and they not marked on map, unlike other tasks.
I split a guide on locations, because if write everything in one pass, it will too big. Maybe I combine everything into one later.
Items are listed in the order, which they are encountered throughout the game. Of course you can always go back to the desired location and to find the missing items.

Challenge: Sun Killer.
Location: Research Base.
You need to find medallions, hanging in different places of this level, and destroy them by shooting. There is 5 medallions and you need find and destroy them all.

To get inside base first you need pass a cavern. In moment, when cavern is ended, an base is started, you will find a big square hole in floor. Medallion hangs above this hole.

Go forward until you find a campfire. From this room you can go ahead, or break the door. Both ways lead you in corridor with water and corpses. Stay in center of corridor and turn back (or jump down, if you choose door, and turn left). Medallion hangs above entrance in this corridor.

Return to the room with campfire. Now we need to take a close look on door, which leads to corridor with corpses.
Break this door, but not jump down. On opposite wall you will see a window. Through this window you can climb in secret room, but not do it now. On opposite wall of secret room you will see a crack.
If you take a look through door > window > crack, you will see a medallion. Place, where this medallion is hanging, is unreachable. And point before the door is only place, where this medallion is visible.

Proceed, until you find a elevator. This part requires solve a puzzle. After you throw elevator down, jump down too, pass elevator platform and turn right. Medallion hangs under a catwalk, which go around elevator shaft.
You can see this medallion when you just find a elevator. Turn left and go down the stairs. Soon you find a dead end with door. Through a window in this door you can see this medallion.

Go forward and look on right wall all the time. Soon you will find a chain-link fence with some machinery behind. Medallion hangs behind right part of this fence.