Finding Barba[edit]
Barba is probably a little bit easier to find if you head away from the gathered light. From the temple head southeast through the ravine until you reach the southern part of the map. From there head due south and round the tip of the raised land to your right. From there, turn west and make your way across the desert. Barba is located at D-6 of your map, just at the edge of the desert in a large artificial structure.
Defeating Barba[edit]
Barba, the Bearded Giant, lies locked away underneath an ancient temple and is the most aggressive of all the colossi thus far. When you reach the ruined floor however, his stone prison will open (via cutscene) and the malicious giant will immediately begin to chase you through the temple. The best strategy for this first stage of the battle is to run away. Head towards the small barriers opposite the wall Barba came out of and quickly climb over them by jumping and pulling yourself up. Be very quick, Barba will be close behind you, breaking each barrier when he reaches it. Repeat this for the remaining two barriers and take shelter in the temple ruins against the wall. Barba can't get at you here so you're pretty safe if you need to rest (in case you took some damage getting there).
If only you could stay here, protected, and defeat the colossus... Unfortunately, you must still scale the giant. Grab Barba's attention by firing an arrow at him (preferably at his chest or face) and wait inside the temple ruins. He should eventually bend down and peek inside. Seize the opportunity and run at him, jumping and latching onto his beard. Climb up to his head and the first vital. Charge stab a few times at this position until the symbol disappears.
Vital number two lies on the left side of his back. Climb down to the symbol (or try dropping down and grabbing back on; he tries hard to shake you off so climbing down can be difficult), and perform a few more charge strikes. With any luck, Barba should go down fairly easily and without knocking you off once.
Hard Mode Strategy[edit]
You likely will have much less stamina for this fight than before. You can rest by standing near Barba's spine to recover your stamina. Well, now that you've finished off the first two weak points, you'll need to completely get off Barba. Drop down and hide back under the temple. If you need to grab his attention again, fire off another arrow. When he peeks inside once again, DO NOT go for the beard; instead, head for Barba's left hand (the one on YOUR right) and let him lay it flat on the ground. Climb on top and he'll get up and start trying to shake you off. He'll do this often, so fully charged strikes are impossible. Just go for short charged strikes until he finally falls.
Time Attack Strategy[edit]
Barba is a tough time attack because of your limited stamina and the first minute or so of the fight you'll be leading him to the back of the temple. Once you've grabbed onto his beard, hit the vital on his head first, it's the closest one. Don't try to charge up all the way, instead use half to three-quarter charged stabs, because Barba will try very hard to get you off his head. It's critical here, especially in hard mode, that you be able to climb back up and rest yourself by standing near Barba's spine in between his shoulders to regain your stamina. Taking the few seconds here is worth it. If Barba bucks you off, it'll be nearly impossible to make your time. Finish off the vital on his head then head to his lower back. Also make sure you stop to rest again at his spine until you have full or nearly full stamina.
If you're in hard mode it's doubly important that you hit the back vital last. If you try for his head last and jump off in front of him, he'll smash you before you can recover from the fall. Drop off behind him and scramble back underneath the shelter. Hit him with a few more arrows until he stoops down to check it out again. Immediately head to his left (your right) hand and jump on it when it lays flat. You only get about one second to grab it before he lifts it back up again, and its important that you do it right the first time. Hit him two or three more times to finish him off.