It's pretty hard-core, I've never done it myself.

It was a popular self-imposed challenge on our forums, so I threw some achievements up for it.

I imagine it's just a LOT of grinding.

A strategy that worked well for me so far is:

Ice Mage: Boost Chilling & Freeze first
Knight: Boost Armor Piercing first
Healer: Boost Healing & Blindness first
Berzeker: Boost Frenzy, Madness & speed Increase first.
Bowman: Less important for my strat, but I tend to boost critical & Armor Piercing first

Then, I setup the ultimate melee team: I pick a path where I know the enemy will go and I place a knight, then ice mage, then berzeker.

I tell the knight to hit the most HP/Armor target while telling the ice mage to max effect and leave the berzeker on default.

I try to place the healer to cover my entire team, but if it cannot, the knight and ice mage get priority.

Basically, the healer is for protection. He will heal allies and blind enemies to make their attacks less effective.

The knight will destroy the armor.

The ice mage slow down the target.

And finally, the berserker will inflict massive damage on slow moving unarmored targets.

I often place the archers in a nice place to mop up whatever manages to get past the melee team.

Alternatively, you can place them to complement the berskeer's melee with arrow and make the kill zone event deadlier.

Overall, I'm a big fan of passive skills, because while the higher level attacks are very nice, they eat up a lot of psi so you cannot give them to most of your team anyways.

My advice:

A. Get all units ASAP, you can grind scrap and units get equal XP (doubled if fielded) even if sitting in the sidelines. So buying up all units early gives you more levels to all units.
B. No need to get too fancy for basic campaign... only if you want to go NG+
C. Always get the 1st level of any ability, 1st level is always a big booster.
D. 6 maxed out archers rock in regular, become near worthless in NG+ due to massive anti archer resistance.
E. Ice mage is the most powerful unit in the game. Focus on AoE.
F. Be aware of the immunities and resistances monsters get in NG+... it brreaks a lot of the earlier strategies.

Ok, so in order to do a mission advanced mode, I need to XP farm a bit, don't I? I can't just jump in on the first try level 3?

You can try, but you will most probably fail. I might be a good advice to return to the former levels after finishing a chapter. That way it will still be challenging and not too easy.

Look at creep levels at various difficulties. This will give you a general idea of when it's best to attempt a particular challenge. E.g. if you have just cleared 20-25 level creeps on Normal (the mines exit), it makes sense to go back to 20-25 on advanced (Knights) and expert (Hospital), respectively.