This solution may be a bit long winded so bear with me.
First make sure you choose Extreme at the beginning of the game. Once that's done, do not change the difficulty.
First, I'll go through the character build I used. I tried it with a Warrior and relying on melee doesn't work for this mode. Mages take too much damage in the early stages. The best class is Technical.
AttributesMake sure you evenly spred the points between Accuracy and Endurance until they are both level three. Then use the next two on Accuracy and the two after that on endurance. For the purposes of this build, any you gain after this, should be put in to Willpower.
TalentsLevel three Science is your first port of call, this allows you to make your own bullets whilst also trippling the amount you make at any one time.
Second is Vigor level three. Then Lockpicking Level 2 (Make sure you breastplate strap has at least the level 2 lockpicking kit, to boost the skill to three)
Then Intuition two.
SkillsUnlock them in this order:
TechnicalPrecise Callibration
Destructive shot
Impact Bullets
Rifle
Roll
Galvanising Fury
Vengeful Fury
Backstab
Set Trap
Fast Traps
Destructive Elemental Preparations
Seismic Magic Preparations
Economical Alchemy
Phial Throw
Light Grenades
Mephitic Charge
Extended Statis Alchemy
Devestating Grenades
Bomb
Powerful Bomb
Toxic Bomb
Magic skillsStasis
Stagnation
Corrosive Emnation
Perfect Incantation
Chystalisation
Magic Healing
Purifying Healing
Devine Aid
Steel healing
Group healing
Tech SkillsAnointed Weapons
Alchemical Dose
Assassin's Touch
Focused Alchemical Fire
Alchemical Earthquake
Magic TreeShield of the Enlightened
Steadfast Light
Shield of Fury
Holy Bulwark
Blessing of the Enlightend
Storm
FightingKeep your distance and use your rifle (you can use a pistol if you find one you really like) When the fury gauge is filled out, use Bomb.
Use roll when you spot an enemy about to attack to avoid damage.
Try to use Magic Healing to keep your companions and yourself with a bit of armour during the fight. Use resusitation powder if one of them falls.
Don't use traps after you've unlocked Phial throw. Hot key a few bombs to your quick skills (I had poison on

and Magic and elemental on

+

and

respectively.
We aren't going to use coating as it is fairly useless on Extreme but it does unlock an extra tropht and means you won't have to do an extra playthtough to get it.
Where possible in the wilds, use Assassination to eliminate as many enemies from big groups as possible fairly early. You do this by pressing

to couch and sneaking up behind an enemy and pressing

when prompted.
keys
Directional pad
= Light

= health potion

= Poison Phial Throw

= Fire Rifle/Pistol
R2 Keys
= Magic Phial

= Elemental Phial

= Bomb

= Healing Magic
If you want to (and don't feel lile using the tactical pause menu), you can replace Poison Phial with Statis, if you find that more useful as Stasis is particularly good in boss/guardian fights to stop them from using certain attacks.
CompanionsUnless you're doing a side quest for a certain companion, I'd suggest taking Siora and Aphra most places with you (before Aphra is available then use either Petrus or Vasco)
Kurt is a Warrior and can be a pain to keep alive, although he's very good for helping you strip down a boss' armour rating.
Siora has some nice buffs that she provides and is also a pain to keep alive but her buffs are very helpful at times.
Aphra is one of the least painful to keep alive, she's a technician like ourselves on this run, so kitting her with a very powerful pistol of weapon is a must.
Make sure it's different to yours though i.e. If we are doing high damage output, shhe must do high armour damage output.
Vasco is similar advice to both Kurt and Aphra. The advantage of Vasco is some situations over aphra is that he can do melee damage and run away to use his pistol, like we can with our main character. Without Really good armour and armour upgrades though, he does tend to take a lot of damage when he goes in to melee mode.
Finally, Petrus, He must be given a high level ring if you're going to use him. He must be given as higher leveled armour as you can find him, with nice upgrades, chest plate for amour/balance upgrades and the rest of his armour should focus on resistances.
During this playthrough, I went as far as doing
QuestsMust do ALL companion quests and keep Kurt alive, must do as many side quests as possible (Go for either having every faction at at least Nice or all at friendly for the endgame).