How can I detect the death of a mob in Minecraft version 1.16?

I don't remember if the deaths scoreboard works for entities other than players. If it does work try that. If that doesn't work try using

execute as @e[boss selector goes her] at @s store result score 'i forgot the syntax for store in execute' run tp @s ~ ~ ~ 

and if the score is = 0 then the boss is dead. The following video shows you how to count entities. His method may be better.

Give your boss a custom loot table, using the DeathLootTable NBT tag, that drops a special item (potentially with custom NBT tags, like lore, so that it cannot be counterfeited). Then make the next part of your map contingent on the player surrendering that item (use an item sorter to check that they have in fact surrendered the correct item).