"Bastard" is cultural minefield. How bad a word is it? It depends on the context, how it is said, and which of its many meanings it has.
I couldn't find the audio, but apparently Yatsenyuk called for international support "to bring to justice all these bastards who committed this international crime." He shows how strong his feelings are by letting his language get SLIGHTLY out of control and go SLIGHTLY out of bounds.
"Bastard" is not taboo, it is not vulgar, it is standard English. However, its main meaning is a disagreeable, mean, offensive, cruel person. If it is said seriously, it is a bad insult.
Like other bad insults, it CAN also be a friendly joke. "What, you've got tickets to that concert? You lucky bastard!"
To make things more complicated, it has a perfectly straight meaning of "small" or "not standard size." There is a carpenter's tool called "a bastard file."
It has the meaning "illegitimate," meaning a child born to a couple who are not married--often, a married man's child born by a woman who is not his wife. By extension, it can mean anything mixed up in an incorrect way. So, there is a perfectly acceptable word, "bastardized," meaning something corrupt or debased. "Real Greek yogurt is good, but watch out, there are a lot of bastardized versions of Greek yogurt in the supermarket today."