Your initial thoughts are correct about the armor.
This link describes how to kill a brute and offers a brief video with some general info.
http://www.ign.com/wikis/mass-effect-3/Brute Brute's defenses consist entirely of a yellow Armor bar.
To deplete this you can use fire-based attacks and Powers meant to reduce armor.
The most important thing to remember is to keep your distance.
Stay behind cover and roll out of the way when it nears you.
If it hits you, your shields will evaporate.
Hit it with Grenades and other explosives.
Armor Piercing Rounds and Disrupter Ammo are good to help reduce the armor, but explosives can momentarily pause the creature, giving you valuable time to get away.
The other thing I've been doing a lot is saving my grenades for large enemies and bosses only.
I've really only had to deal with brutes and atlases so far, but having grenades while your other abilities are in cooldown makes a big difference.
gaming.stackexchange.com/users/20974/Steve the Maker
As with most creatures, Aim for the Head!
Specifically, you'll want to aim for that Turian head grafted onto the front of the Brute.
Nail it right between the eyes, and it won't last long.
gaming.stackexchange.com/users/3129/LessPop_MoreFizz
As a Sentinel, I've found that the Lob Grenade power is extremely useful, particularly when you're being surrounded by multiple brutes.
3-4 grenades should drop them to almost 1/4 of their armor strength.
Couple of shots of Warp interspersed with Lob Grenades should make mincemeat of the brutes.
Also, do run away from brutes - climb the ladders, brutes can't climb them.
Close/melee encounters with the brute will leave you in jelly in no time
gaming.stackexchange.com/users/200/Sathyajith Bhat
Vanguard with fast power recharge could easily melee even groups of brutes.
(At least on normal difficulty.)
Just charge, hit, roll side-way and charge again.
Repeat until brute is dead.
One thing: Do not charge while brute is about to pouce.
It will interrupt your melee and drop your shields.
gaming.stackexchange.com/users/13444/Korusef
The soft spot is the exposed spine just behind the head.
Not as much armor plating there
so you can knock a good chunk of his armor down.
gaming.stackexchange.com/users/23442/Koka
with the vanguard, you can easily kill numerous brutes using charge and nova.
just make sure you have a fast cool down and you move back or sideways before you nova.
thats if you got the radius for nova.
same tactic with banshee
gaming.stackexchange.com/users/30965/Anjo
The Brutes are giant Reaper-Giant hybrids that are very well armored, to the point where I'm sure their entire health bar is their armor.  However, it seems to me that there is a certain point where it is most weak against my shots but I am unable to figure out which part of its body to aim for.    Any suggestions?
How to kill a Brute effectively
gaming.stackexchange.com
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gaming.stackexchange.com/questions/54134
gaming.stackexchange.com/users/12823/Tablemaker
Lob Grenade power is very useful and you should aim for the head. The soft spot is the exposed spine just behind the head. Seems like each player has a different approach to tackle Brutes.
The community is detailing few tactics that work against Brutes.