Radioactive Bears (sometimes called Rad bears) are modded bears that are very difficult to kill. There are three classes that determine the level of difficulty to kill them:

Tough 5,000 hit points - Least difficult to kill but still much more challenging than Vanilla bears.
Beast 10,000 hit points - Medium difficulty.
Juggernaut 20,000 hit points - Extremely difficult to kill.

Compared to:
Vanilla bears - 800 hit points.

Rad bears can be recognized by their glowing eyes and green mouths. They are brown in color with unkempt fur. They behave the same way as regular bears. Tactics that you would use to avoid or to hunt regular bears will work on Rad bears as well other than the difficulty to kill them.

Rad bears are confined to their spawn areas and will not roam away from them. Therefore you do not have to worry about them wandering into areas where they are not expected to be found. There is an exception though - if a Rad bears has noticed a player and is in attack mode, it will follow that player wherever the player goes. Rad bears in attack mode are NOT confined to their spawn areas. 

You may not run over Rad bears with your vehicle or helicopter. If you attempt to do so, your vehicle will be damaged and you will not be able to drive/fly it until you have repaired the damage. They will not damage a stationary vehicle only one that is in motion.

Do not attempt to engage Rad bears unless you have heavy duty weapons and adequate ammunition. Killing them requires huge amounts of ammo. Also be sure to bring weapon cleaning kits and bandages. It is best to hunt them in teams.

Why would anyone want to hunt these killers? Because their pelts and meat are very valuable when sold at the Black Market trader. Sale prices vary:
Pelts: 600 -1000 each
Steaks: 160 - 200 each
** Juggernaut bears yield 4 pelts instead of two pelts