My suggestion is to make a scoreboard dependent on deaths to a certain mob. then test for if the mob has one death then use a comparator to activate what you want. If its a custom built boss, use a redstone health bar and at the end attach the redstone to whatever you want to activate.

Thankyou to all who helped i solved the problem and the map will be realeased in a matter of time, sorry for bad grammar

use a command block with the command
/testfor @e[type=YourMobType,name=YourMobsName]

I don't know of any ways to activate stuff based on mob names, but you could have a hopper where you put the mob's drop into. If a you are using a Wither as a boss, you can have a Nether Star as the "activator", or something like that.