Its possible for radiation to damage life, but it's harder to wipe it out, and it's just not possible for it to happen on a galactic scale.
A gamma ray burst is a massive explosion that releases huge amounts of Gamma rays in a beam. We have observed very distant ones, from half-way across the observable universe. Fortunately, we have not had one close to us, since it could kill a large fraction of land life. However, gamma rays are not very penetrating of water. They can travel a metre or so before being blocked. So animals under the sea would probably survive. Those animals that weren't killed outright would be hurt by the collapse of food chains and the damage to the ozone layer. But I don't think you can kill all life this way.
Heating the planet to boil the oceans would probably kill nearly everything, but this would require a massive amount of energy (10^25J). If you took all the energy of the sun over two years, it would be enough to boil the oceans, and probably kill all life. A nearby supernova could do this, but there wouldn't be a habitable planet left afterwards, it would probably kick start a runaway greenhouse effect. It certainly would take some time for the world to cool, even if this is avoided.
Such an event can't happen galaxy wide. For a start, the galaxy is so big that it would take 100000 years even for light to cross it. And the scale is much bigger. It has a cross section that is 10^28 times bigger, so you would need 10^28 times more energy (10^53 J). This puts it outside the realm of reality. It is the sort of energy you get if you make every star in the galaxy into a massive giant star, and then make them all go supernova at once.
Becoming more speculative. It is sometimes hypothesised that the physics of the universe are not truly stable, and could change False vacuum. A bubble of new physics could spread out from a point at the speed of light. Now usually we suppose that this bubble of new physics would be fundamentally different from our universe, but suppose that the new universe was identical, except that gold was highly radioactive. The tiny amount of gold that we have in our body (0.2mg) would breakdown in radioactive decay in a few seconds, subjecting us to a massive radiation dose (about 1000Sv) The same thing would happen to the rest of life. The planet would be sterilised, and the bubble would spread, killing of any life in the universe (given enough time) New life could evolve inside the bubble. However, nothing could travel into the bubble if it had even a trace amount of gold. And there is no way for anyone to know of the existence of the bubble in order to prepare for it.
This scenario is not scientifically plausible, but if you wave your hands fast enough, people might not notice.