For "Top of the Food Chain", You must kill a legendary boss in Warzone.
(Looks like the top solution was edited to include Firefight after I posted this)
There is a NEW and EASIER way to get this achievement as of April 14th 2016: Firefight!
In Warzone Firefight, A team of 8 spartans fights through 5 rounds of AI enemies. During the course of the match there will be many legendary bosses.
A legendary boss in identified with a yellow mark next to the name of the boss (There are some elite Legendary bosses with a red mark).
The traditional way (normal Warzone) of obtaining this (which is covered well in other solutions) can be very frustrating. You must be the person to get the last hit on the legendary boss to get credit for the kill and the achievement. You would have to compete with teammates for the kill, while being targeted by the boss and other AI enemies, and the entire other team of Spartans. There would only be one legendary boss at a time, so the chances of getting the final kill will always be slim.
In Warzone Firefight, there will not be another team of Spartans trying to kill you, less teammates of your own, and since there are tons of legendary bosses... you have a much better chance of killing one. In fact, when I got my achievement, I believe that I was just lending support with the machine gun turret. Like other guides have mentioned, saving up your req points for heavy vehicles or big weapons would help take out these bosses.
*If this solution helped you in some way, please vote positively. If you think it needs improvement, please let me know how in a private message or by leaving a comment.*