So two very kind users gave me a few tips on how to improve my party. They are getting in some nice hits now.

However, even figures like the Rogue Mage from the Task Lists are taking at least half my pets health in a few goes.

Mei is my Tank. Water proficiency, Legendary Assassin gear (Evoker Relic).

Shadow is my Mage, Light proficiency, Legendary Evoker gear (Myrmidon Relic).

Dusk is my Cannon. Air proficiency, Legendary Myrmidon Gear

What can I do to make them better?

Here's their stats:

Mei:
Health: 10,580
Level: 60
Physical Damage: 487
Magical Damage: 99

Strength: 454
Intelligence: 197
Dexterity: 199
Agility: 294

Physical Mitigation: 34.09%
Magical Mitigation: 28.56%
Critical Hit Chance: 17.48%
Accuracy Bonus: 11.26%
Avoidance Chance: 14.47%
Quickness Rating: 49.30

Shadow:
Level: 60
Health: 5,061
Physical Damage: 99
Magical Damage: 523

Strength: 198
Intelligence: 526
Dexterity: 288
Agility: 202

Physical Mitigation: 21.86%
Magical Mitigation: 29.78%
Critical Hit Chance: 22.86%
Accuracy Bonus: 15.01%
Avoidance Chance: 11.38%
Quickness Rating: 49.00

Dusk:
Level: 60
Health: 4,881
Physical Damage: 430
Magical Damage: 283

Strength: 470
Intelligence: 175
Dexterity: 326
Agility: 176

Physical Mitigation: 25.94%
Magical Mitigation: 20.29%
Critical Hit Chance: 25.86%
Accuracy Bonus: 16.05%
Avoidance Chance: 10.40%
Quickness Rating: 50.20

Hmmm. Well can you survive the battle with the Rogue Mage? No matter how much he takes your health down, surviving is really the only goal.

I can only tell you where my party differs:

My physical tank has more points in Agility - this helps mitigate damage and raises their chance to avoid attacks. She is just my damage sponge.
My canons have all their stat points in their attack skill (int or str) with just a bit thrown into dexterity for higher critical hit chance. The faster they go down, the fewer times they can hit you!
If you wanna take a look stable 1, tab 1 Vivianne, Gwendolyne, and Petunia right at the top.

For a normal exploration party the two cannons don't take many hits so giving them a bunch of extra health doesn't really accomplish anything.

And obviously it would be best to get the correct relics when that is possible

Last but not least, farming Dungeon of the Forsaken for mythical gear will up their stats a bit too!

Yes, they have survived the rogue mage battles.

I think I'll try to re-stat my pets like yours are, and find the correct relics. :)