METAL GEAR SURVIVE

In addition to the tips provided.

BIG MOUTH
Locations:
Campaign- Map 1 right of Transporter 5 in a circle of rocks.
Co-op- Rescue Mission: Forsaken Ruins.

You can lure Big Mouth to the green fenced gate. It won't go past this fence. From there, you can dodge behind the 2 pillars outside the fence and wear down Big Mouth with whatever weapons you bring.
Have plenty of shotgun shells, O2, Kuban, variety of repair kits and any other ammo, because the fight takes some time. I also used molotovs, fire arrows and turrets, but turrets can be destroyed.
Shotgun blasts to the mouth/head do huge damage, but requires close range. Look for when the monster tires after attacking you. It droops its head a few moments, giving a chance to attack.
For another achievement, remember to try and get him to swallow an exploding Barrel.

FROSTBITE
Locations:
Campaign- Map 2, just south of Transporter 7.
Co-op - Rescue Missions: Fallen Village.

The same technique can be applied here. The boss will not go outside the fenced area.
I unloaded molotovs and flame arrows on the boss until I ran out. Turrets can be easily destroyed. Eventually I used my Scout class invisibility and nailed him with the shotgun. Also, while invisible, you can stand underneath and hit its appendages with a melee weapon.
Its weak point is the small tentacles glowing red in the middle of its body. They cycle around.

After beating the main story you can randomly find a red circle on the Dite map that says "powerful enemy detected". If you go there you'll find an enemy called Big Mouth. The second boss is on the FOB map near teleporter 7. I believe you have to kill the first one for the second one to spawn. Sleeping in a tent to advance time may help to get one to spawn.

Some tips for fighting the first boss. If you are using the scout subclass the stealth ability and fox step ability will let you easily clear all the basic wanderers in the arena and place some barrels. A purple shotgun with about 70 rounds should be enough to kill him. His first phase is pretty easy if you don't have any additional enemies, just hide behind a pillar in the arena and when he's not shooting you can pop out and shoot him a bunch. After he staggers from the shotgun he'll usually try a bite attack so you can place a barrel at this time if one isn't nearby. His second phase is a bit harder since his attack is a bit more instant but you can use the cloak to get in free hits and then hide while waiting for it to recharge.

Second boss is actually a lot easier, I forgot to refill my ammo after fighting the first one. I brought a purple shotgun with about 70 rounds and a purple sniper rifle with no extra pouches; I only used about half the ammo I brought so this should be safe. Again as an invisible scout just quickly clear the extra enemies. Then hide near it and watch the top of the main section for one side to glow orange. Hit that spot with the sniper and hide again. Wait until a section goes orange again and shoot it and it should stagger the boss knocking him to the ground. Then you just have to run up to him and unload your shotgun into the his main section (which should be glowing orange) until he gets back up. Then just repeat these steps until he's dead. If he ever spots you just go invisible and hide behind a building so he loses you.