Giants' Memories
The Ashen Mist Heart allows you to access the three memories of giants. You should have obtained the Heart from the Ancient Dragon at Dragon Shrine. Upon entering a giant's memory, you have a limited amount of time to do whatever you need to do. When your time limit is exhausted, you would be forced out of the memory. However, you can revisit a memory at any time. The purposes of visiting the giants' memories are twofold. First, you want to collect all Souls of a Giant. These will be used to complete Vendrick's quest line. Second, you want to obtain the Giant's Kinship, which is required for unlocking the fight against the final boss.
Memory of Vammar
77. Memory of Vammar, Dark Souls II: SotFS
This memory can be accessed by interacting with the tree-like giant corpse located near the Cardinal Tower bonfire. Your objective should be to grab the Soul of a Giant from a giant's corpse. Exhaust the dialogue of Captain Drummond to initiate his quest line.
Memory of Orro
78. Memory of Orro, Dark Souls II: SotFS
To access this memory, interact with the giant corpse located at the end of the arena where you fought the Pursuer, i.e. the arena with two ballistae. You should see Benhart sitting near the giant corpse. Exhaust his dialogue here, then enter the giant's memory and exhaust his dialogue again. Your next objective should be to collect the Soul of a Giant near the end of the memory.
Memory of Jeigh
79. Memory of Jeigh, Dark Souls II: SotFS
This is a boss fight against the Giant Lord. Defeating the Giant Lord would reward you with the Giant's Kinship, an item required to unlock the final boss fight. Leave the Giant Lord alone until you are ready to face the final boss. The Giant Lord is weak against dark. Buff your weapon with Dark Pine Resin or Dark Weapon. To complete Benhart's quest line, summon him for this fight and make sure he survives the fight. Don't summon Captain Drummond, otherwise you won't be able to summon Benhart.
Defeat the Giant Lord and revisit Captain Drummond within the Memory of Vammar. Exhaust his dialogue and he would gift you the Drangleic Helm. You would still be rewarded even if you didn't summon Captain Drummond for the fight against the Giant Lord. Also revisit Benhart in the Memory of Orro and exhaust his dialogue to receive Benhart's armour set and weapon.