Checkout missable achievement "Chop Chop Chop" to kill Belyash in a specific way. However the "Medium Rare" achievement to simply kill him is non-missable.
You encounter Belyash during the mission "The Show Must go on" as you reach the Theatre. The Theatre entrance looks suspiciously like a boss arena and this is where Belyash will spawn.
Thankfully Belyash is a relatively easy boss fight. He has slow obvious melee attacks and lunges, the only thing that might catch you out is the ground pound similar to what Hedgie used. Just jump over the orange shockwaves to avoid damage. Once Belyash drops down to 50% health he'll start using a flamethrower attack that also sets the grass on fire. While he's spraying try to get behind him to land a few blows.
Once he goes down, you should get the achievement. If not, load a previous save to try again and hopefully it pops the second time around!