At the beginning
At the beginning the character has 3 life flasks then he finds another one at the body in the Cemetery of Ash.
First estus shard placed at the roof of Firelink Shrine you can reach it by buying a key from Shrine Handmaid or by jumping the roof using a tree. If you used “key option” you need to jump on the roof and find a pass under the roof. The estus shard will be on the body at the left.
High Wall of Lothric
Second shard will be at the High Wall of Lothric after the second bonfire go straight to the second ladder, turn left and go to the room with shield knight go past him the estus shard will be at the room with dogs at anvil.
Third, you can find it at Undead Settlement near fired tree.
Road of Sacrifices
Fourth will be at the Road of Sacrifices. After bonfire forest of torment go to the entry of the fortress and turn left, jump down and pick up estus.
To find fifth after bonfire Farron Keep go forward to the broken bridge estus shard will be near slugs.
Cathedral of the Deep
Sixth located near the second bonfire at Cathedral of the Deep to get it go forward to praying hollow estus shard will be near them.
So where to find remaining estus shards in Dark Souls 3?
Seventh will be at the location Smouldering Lake at the room where the bonfire Old King's Antechamber find illusory wall and go straight to the end of the corridor. The estus shard will be there.
Eighth located at the Anor Londo if you stay back to main doors then the chest with estus shard will be on your right.
Ninth will be at the Irithyll Dungeon. After the bridge with 2 crossbows you will find the chest carefully. It’s mimic with estus shard to neutralize him you can use Undead Hunter Charm.
Consumed King's Garden
Tenth placed at the Consumed King's Garden. After bonfire Dancer of the Boreal Valley go up the ladder turn left use elevator and before it arrives jump to platform estus shard will be on your right.
Last one will be at the Grand Archives. After the bonfire Grand Archives use the elevator on your right then go up to the roof estus shard will be there.
That was all locations where you can find estus shards in Dark souls 3.