The following spells are the core spells you will need to succeed.

Precision
This spell increases the damage dealt by shooters by a certain percentage. The increase depends on the casters intellect and his "Creation" skill.
This spell is weaker at lower levels due to low intelliect. Always calculate if the minimum damage of your troops already matches its maximum damage (or more) with the use of this spell. If that is the case, you should cast this spell in the first round.

Blessing
This spell causes your troops to deal only their maximum damage.
At low levels, this spell is better than Precision, because the only scalable thing in this spell is its duration. Usually cast in round 2.

The following spells synergize well with the archery build.

Resurrection
Heals and resurrects a certain amount of units in a selected troop.
If you happen to lose some units in a troop, you should totally reduce the losses with the help of resurrection.

Trap
Places an invisible Trap on the battlefield that deals a certain amount of damage to any troop walking in it. The caught troop loses its turn.
This spell is more of a goodie. It prevents that your enemies storm the way through to you too quickly. There is also an ingame achievement which places traps on the battlefield and increases trap damage if troops are killed by traps.

I will only list the essential skills and without description. You can look it up on your own ingame. I will however add some notes about why I take said skill. The skills will be in order of highest to lowest priority.

Might

Quick Draw 3
An increase of your archers initiative assures that they can shoot the enemy before he can act. The attack boost is only beneficial.

Onslaught 3
Assures that you always get the first turn for all of your units. The adrenaline increase is good for your orcish units.

Action Rage 1
On rank 1, this skill transfers adrenaline only to level 1-2 orcs, so your goblins will make most use of this.

Berserker 3
Dealing double damage occasionally can save the lives of some of your units.

Only Heroism is worth taking in the Might skill tree as an addition.

Mind

Persuasion 1
Elves dislike orcs and Vikings, of which you will have both, so this skill needs to be on 1.

Edda 3
The song of Asgaard makes your troops ignore a part of the enemies' resistances but lowers their defence.

Diversion 3
If an enemy ranger skips his first round's turn, you don't need to shoot him in the first round, granting you some time.

Sense Weakness 3
Increases critical hit chance for your units. More criticals, more damage.

Jarl 3
The leadership bonus may appear small at first but it will pay off in the end.

Oratory 3
Some additional morale does never hurt.

Every other skill is only a drop on the hot stone.

Magic

Distortion Magic 3
You want to cast the spell precision, right?

Order Magic 3
And blessing too I guess...

Creation 3
Greatly increases the effectiveness of Precision.

All intellect boosting skills are very good, but not vital. Transmute 2 may save you some waiting time between battles.

Ranger
A good Sniper, shooting enemies efficiently at any range. Ineffective against boned enemies.

Elf
Similar to the Ranger, but generally lower attack. Has a very useful ability to double his damage though and inflict more damage than the Ranger.

Bowman
Not the best archer, but his slow arrow is good to keep a fast enemy on range and both special arrows are good against ghostly creatures.

Goblin with Catapult
Those goblins have a very powerful area of effect attack every 4 rounds. Damage is pretty good as well in effective range. They are excellent against boned enemies. Furthermore, they recruit Goblins, Irascible Gobilns or Shamans after the fight.

Goblin
The Axe throwing goblins are excellent against boned enemies. On high adrenaline levels, he probably deals the highest single target damage of all ranged units. On adrenaline level 3 he gets a ghost axe, which may be thrown efficiently at any range and deals even more damage.

Shaman
The Shamans throw ghost axes, which travel any distance and ignore resistances and 30% of the unit's defence. Pretty good against heavily armored targets. Even though not classified as shooter, the same bonuses apply. Pretty bad base damage with only 1/3 of the damage of a goblin.

Beholder
A good magical shooter with control elements.

Evil Beholder
A good magical shooter with control elements.

Cyclops
A sniper unit with low damage potential. At least it is more durable than your other ranged fighters. Precision does not apply on Cyclops.

Slinger
In general not a bad unit, but it's really low attack value makes him only average against big enemies.

Canoneer
His high attack value doesn't make up for his worthless damage output. Improved quite a bit by the DLC.

Thorn Hunter
An average shooter, but Precision does not apply on it.

Royal Thorn
A good shooter, but Precision does not apply on it. Can spawn Thorn Warriors or Hunters every 3 rounds.

Repair Droid
An average shooter which can escape quickly due to his high speed. Precision does not apply however.

Fire and Ice DLC

Avenger
A good shooter with controlling elements.

Scout
A good shooter with slowing arrows.

Contemplator
A very strong magical shooter.

Gorgons
An average magical shooter with controlling elements.

I would strongly recommend to use the following units:

Elf - Goblin - Slinger - Goblin with Catapult - Ranger
Reserve: Slingers and Goblins with Catapult.

For DLC:
Contemplators - Rangers - Avengers - Elfs - Gorgons

You can fill up slingers and Catapults any moment. Goblins don't need to be refilled as they are recruited by the Goblins with Catapult anyway. For the elves, just sail to Merlassar once in a while and restock your troops.

Generally you should keep an eye open for the following items, but you will probably not find them all in the whole game, so focus on attack, intellect and Leadership.

Elven Bow
Type: Weapon
Race: Elves
Found in: Unknown
Description:
+5 Attack for Bowmen
+10% Damage of Critical Hits
+25% Chance of Critical Hits
(Greatly increases your criticals' potential)

The Black Headband
Type: Helmet
Race: Elves
Found in: Unknown
Description:
-5 Attack
+25% Critical Hit chance for Elfs and Rangers
+15% Critical Hit Chance of Arrows fired from a bow
(40% a real damage boost for your arrow firing elves)

Marshal's Baton
Type: Regalia
Race: Human
Found in: Unknown
Description:
+1000 Leadership
+1 Morale to all humans
(There are no real good Regalia pieces for an archer, so more archers mean still more damage)

Odin's Flag
Type: Regalia
Race: Vikings
Found in: Unknown
Description:
+150 Leadership
+20% Attack for allied troops
+1 Morale of allied Vikings
(Attack increase, must have. Multiple Flags don't work for some reasons)

Belt of Strength
Type: Belt
Race: Vikings
Found in: Unknown
Description:
+25% Attack of allied troops
+50 Leadership
+1 Defence
(Good as an attack booster)

Cloak of the Dark Lord
Type: Armour
Race: Undead
Found in: Recipe / Random
Description:
+2 Attack & Defence
+350 Leadership
+7 Mana
(Leadership, Attack and Mana, that's what you always need)

Combat Boots
Type: Boots
Race: Vikings
Found in: Sold in several places
Description:
+1 Defence
+3% Critical Hits
(Critical Hits are important)

Shamanic Doll
Type: Artifact
Race: Orcs
Found in: Sold on Freedom Islands (Random)
Description:
-2 Initiative to all enemies
(Never lose your initiative, even if the enemy casts Battle Cry)

Telescopic Sight
Type: Artifact
Race: Dwarves
Found in: Sold in Dwarves' stores (Random, rare)
Description:
+100% Attack for Shooters that use Projectiles or Devices
(Quite an attack boost, does not apply to Eyeless creatures)

I will structure this section into phases. Each phase has it's speciality and uses different tactics for victory. I don't go into detail against certain types of enemies. I mean it is no fun playing archer and a strategy game in general if I tell you every little secret.

Phase I
Your only ranged unit is the Slinger. Use it and your spells and rage abilities to take out enemy archers and mages. You should not rush up to the enemy, but wait for him to close in before you strike in close combat. In case you already have Precision, note that it also applies to Axe Throwers.

Phase II
If you're lucky you find yourself some nice human archers on Vestlig. But for sure you will be able to buy Thorn Hunters. Those are not the best archers and also Precision doesn't apply to them, but at least they are a ranged unit more. You should at least have Slingers, Axe Throwers, Thorn Hunters in your army. It's unlikely that you have the Diversion skill already, but when you have, you will no longer only attack ranged units first, but those that did not skip their first turn. If a ranger skips his turn, you can deal with him in round two.

Phase III
On Fastland you will come across the Warrior Maidens, who have a strong ranged attack every 4 turns. Take them with you. This is already a stage where you should be able to deal with your enemies from range only.

Phase IV
Finally you're free to go everywhere you'd like. As soon as you discover Merlassar (map in an inn in Arlania), sail there and get yourself your two best archers: Elfs and Rangers. In Greenwort you will be able to hire human Archers. On the Freedom Islands you can hire Goblins with Catapults, Goblins and Goblin Shamans.
I would advise you to use Rangers, Elfs, Goblin with Catapults, Goblins and either Goblin Shamans or Slingers, depending on your likes. Note though that taking a third Goblin means that the adrenaline granted from Onslaught will be divided into 3 than rather into 2.

Phase V
This is the final Phase and the needed skills are all applied. You don't have many more ways to boost your effectiveness. You will now have losses from time to time and not always you can heal everybody with resurrection. If you use goblin catapults and goblins and you're in possession of the Skald exclusive skill to revive warriors, don't heal the goblins at all. Heal every other troop of yours, especially those of which you don't carry reserve troops around. At the end of the fight, new goblins will join you. When being on the adventure map again, you get a message saying that X warriors of type Y were revived. Most likely, these will be your goblins. It is possible that you then have too many goblins and you need to dismiss some of them.

This tactic is very deadly as soon as you have access to all units (around level 18, as soon as arrived in Greenwort). The most aweful part is to keep your troops at full stack and find the right items to boost your effectiveness. Undead armies are a bit tricky due to boned enemies, but you'll manage. Enemy heroes are a plague as they usually diminish all of your troops by spells. If played correctly, you will not suffer damage in close combat.
The "Most Damage inflicted" ranking after a fight varies pretty much on what enemies and in which formation you face. I had Elfs and Rangers on the last ranks already, while a slinger did most damage. Very pleasing to see your unit's effectiveness change from battle to battle. In large battles your catapult will just win the struggle for most damage.

Pro's
- High damage at range
- Able to take out enemy shooters in the first round, preventing losses
- Quick battles
- Can defeat any army except for undead, demons and bosses at invincible difficulty without losses
- Every fight is different through different target priorities caused by diversion

Con's
- Not really effective against the undead (boned / phantom)
- Challenging against enemies who evade
- Challenging against demons
- Losses from enemy heroes' spells are above average, due to lesser defence