XII. Enemies and Bosses
The data on their elemental weaknesses was shamelessly copied from GameFAQs, so I'll give credit to grin43, HylianAngel and CPU-Z for compiling all that information. If a mission has no recommended element and gives you trouble, choose a character and weapon that works best against the enemies you will encounter.
Weak to fire: Gibdo, Moblin, Stalmaster, Icy Big Poe, Agitha.
Weak to water: Fiery Aeralfos, ReDead Knight, Lizalfos, Big Poe, Goron Captain, Darunia, Volga.
Weak to lightning: Aeralfos, Darknut, Dinolfos, Shield Moblin, Lana, Ruto.
Weak to light: Ganondorf, Midna, Zant, Ghirahim, Cia, Wizzro.
Weak to darkness: Hylian Captain, Link, Impa, Sheik, Zelda, Fi.
For the above, any attack will do. However, for the big monsters only specific attacks of a combo will do extra damage, i.e. those with a visible elemental effect.
King Dodongo: Weak to water.
Gohma: Weak to darkness.
Manhandla: Weak to fire.
Argorok: Weak to lightning.
Ganon: Weak to light.
The Imprisoned One will always get up once his weak spot gauge has been half depleted, so whether or not he has any elemental weaknesses is irrelevant.
1. When do enemies expose their weak spots?
It usually happens after they perform one of their stronger attacks, so it's just a matter of observing and learning. However, there are a few special cases where you can speed up the process tremendously. Hit Darknuts and Stalmasters with a quick strike and immediately roll behind them. Zant only exposes his weak spot after you've successfully blocked a number of his attacks. Additionally, using your magic and ending it manually by pressing the special attack button will reveal the weak spot of any enemy that is within the range of your attack.
2. What's a good strategy when I am fighting several strong enemies at once?
Besides executing special attacks to hit all of them at once, it's a good idea to play defensively and focus on not getting hit while you wait for a weak spot to get exposed. Not only will you be invincible while a weak spot attack is executed, there is also a good chance that another enemy stands close enough nearby and also takes some damage. Additionally, make good use of the lock-on and switch between targets with the right analog stick; or if you are good, strike enemies without switching targets first.
3. My character's element is at odds with *insert playable character* who is an enemy on the map. Any tips?
If the character in question happens to be one that isn't an immediate objective to defeat, just run away and let them be. You'll be surprised at how good your allies can be at handling the job, so when you return later, there's a good chance that a significant chunk of the character's health is already gone, if they aren't dead already.
4. Depleting the big monsters' weak spot gauge takes so many hits. Any tips besides purchasing upgrades?
Use your special attack. The timer that makes the monster get back up on its feet again will be stopped, so you can do some good extra damage. If you happen to have two special attacks ready (elixirs help, see question 12 in the General section), you are pretty much guaranteed to deplete the entire weak spot gauge in one go (except the Imprisoned One's, he will always get up at the halfway point). It's also a good idea to time the final stage of your strongest combo in such a way that it becomes the first hit of the monster's weak spot (works well against King Dodongo and Manhandla who take some time to fall and expose their weak spot), that way you'll be able to launch another full combo for sure, and therefore your most effective attack is going to hit twice which otherwise might not be possible to pull off.
5. King Dodongo
He's pretty easy to deal with. Stand away at a safe distance and his scream and flamethrower attacks won't even be able to hit you. When he opens his mouth, throw bombs into it. He does so either at random or after performing his flamethrower attack.
Needs to be hit with an arrow when his eye glows blue. This happens either right after a laser attack or when he charges his strongest attack (hit him before he's fully charged). Since you have a few frames of invincibility while dodging, you can move right through a laser attack with the correct timing.
Green tentacles have to be hit with the boomerang. Stand relatively close and hold the block button. His most common attacks are his tentacles shooting stuff at you (no problem when you block, then throw the boomerang after he's done shooting) and all of his tentacles trying to bite you (here they will be green before he attacks, so throw the boomerang right away). The other attacks can be quickly escaped from by pressing back in conjunction with the dodge button to perform a backwards somersault; this usually gets you out of range of both the poison and the mad spinning.
Probably the easiest one because it's more of a challenge to get hit than not hit due to his slow and predictable attacks. Use the hookshot when his tail glows blue.
9. The Imprisoned One
Definitely the most annoying big monster. You have to slash his toes to make him fall while paying attention to the shockwaves he causes with every step. These waves will get more dangerous once his health has dropped below half, so a good strategy is to use special attacks to destroy all toes in one go while being invincible. Use elixirs, destroy yellow pots or cut grass to replenish your special attack bar.
His attacks in phase one are a combination of the other big monsters. When his right hand glows red (King Dodongo), throw bombs at it. When his left hand glows blue (Gohma), dodge the shot and then fire an arrow. When he puts both of his hands on the ground, he is going to mimic Manhandla; you can either block and then throw the boomerang, or throw the boomerang right when Ganon has gotten into position, that you way you can hit his horns before they start shooting; he has two horns, so unlike the other parts, this one has to be done twice. When he begins to levitate (Argorok), start to run around him; after he has finished his flamethrower attack, his tail will glow blue and should be targeted with the hookshot. In phase two, you have to hit Ganon with an arrow when his forehead glows. This happens either right before or after he charges at you. Most of his other moves are rather harmless, but what's noteworthy is that when he swings his right arm for a dual laser attack, it's best to stand still and pity the fool; when he swings his left arm, dodge to either side to avoid the laser that is coming right at you.