Other takedown options:
1 - Explosive Gel on a weak wall
2 - takedown through a glass ceiling (my advice, let his seekers find you hiding in one of the side rooms, then move to the glass above it. DON'T sneak, you need to be standing to get the prompt.)
3 - kick him down, using the line launcher
I think that's all the possible ways to take Frieze down, along with the options the others provided.
e - ohay, Achievement Hunter has released a video as well for the achievement.