
There are 5 new Fontaine unique mobs (or so-called Local Legend) which can be detected with a huge HP bar on top of the screen instead of on top of the enemy. You can see the previous Local Legends here:
All Fontaine Local Legend Locations in Version 4.0
All Fontaine Local Legend Locations in Version 4.1

Table of Contents
Mageblade Corrouge (#1)

You can only challenge this enemy after completing The Wild Fairy of Erinnyes quest so you can reach this location. Teleport to Weeping Willow’s southwest underwater waypoint and swim forward to meet the local legend.

The right ability to fight this jellyfish is by using Ball Octopus’s ability. Every time it produces a white glowing ball, just hold your ability towards it until it backfires on the jellyfish again. To be honest, this is probably the easiest local legend.
Rocky Avildsen (#2)

Teleport to Weeping Willow southeast waypoint and head north towards the small cottage. Extremely heavy DPS, two hits of his can probably kill your character. Have a shield character so you can safely attack him, especially if you’re not a pro in avoiding.
Liam (#3)

Teleport to Weeping Willow southeast waypoint and head northeast towards a small pond with debris littered around. There are many mobs here so you might want to deal with them first so you can focus on this local legend later. He can trigger elemental reactions and it hits like a truck too so have a shield once again. Avoid characters that can inflict elements on yourself like Xingqiu or Barbara or you might do more damage to yourself than the enemies.
Deianeira of Snezhevna (#4)

Teleport to the Tower of Ipsissimus south underwater waypoint and swim southeast towards a ruin. You can only unlock this ruin after completing An Expected Plan quest where you will find the traitor Nacker inside this hideout. Nothing too special about this agent except she has a large HP pool. The skill is also the same as the normal Fatui Operative, just a bit more damage.
Chassanion (#5)

Teleport to the Tower of Ipsissimus south underwater waypoint and swim southwest towards the tower. Enter it through the platform in the middle of the tower. Once you’re inside, swim downwards and you will meet the local legend. This enemy is only available after you complete Search in the Algae Sea Quest where the Tower of Ipsissimus is submerged underwater and water floods in the tower.

It’s basically another Mageblade Corrouge with the exact same skill. Just use the Ball Octopus ability and you’re good.