Any militia with high numbers and bowmen is always a pain to deal with. On competent difficulty, the computer spams the 11-strong brigand guard, which is painfully hard to deal with until late game. Meanwhile, on your first shard, you're stuck with recruits which are only 8-strong and the AI pretty much tears through them like paper.
Here's my strategy on competent:
I buy a wizard, and purchase an altar to get shamans. A wizard is weaker than an scout early on, but a wizard's power grows much faster. Back the wizard up with 3 shamans, and never stop adding shamans. Gems can be a problem on some maps, but I scrounge them through evil choices in random events (like selling corpses to necromancers). Find and exploit mandrake root ASAP to reduce the cost of shamans, or you'll quickly be paying triple price per unit.
Almost all tier 1 creatures have little or no magic resistance, so shamans+wizard will cut through them like butter, allowing you to clear dungeons quickly. Avoid gargoyles, medusas, and any other high MR creatures. Necromancers have high MR, but rotating in a single bowman in your party will let you almost one-shot them. The idea here is to be able to clear dungeons with no losses, because you really can't afford losses until you have mandrake root.
Battle tips on shamans:
Shamans are range 4 units that are basically glass cannons. With enough shamans, you will melt pretty much everything, even Tier-2 units! However, if anything gets in range of you almost instantly die. Careful use of hill terrain (+1 range) and putting forests and swamps between you and the enemy to slow them is necessary. A flat plain with no water or mountain chokepoints is your worst battlefield.
Shamans can even cast a hero spell called curse, which reduces attack, defense, and resistance values. On any creature with a MR of 2 or greater you may want a shaman to curse. In fact, because curse has unlimited range, it's an excellent opener when you start the battle out of firing range.
Shamans's other weakness, besides frailty, is that they only have 4 ammo and it cannot be recharged. Using the curse spell "counts" as a use of 1 ammo. In a battle longer than 6 turns you are dead if you have underestimated the total enemy HP because all your shamans will suddenly lose their range firing ability. When upgrading shamans prioritize hex special>damage>extra ammo>anything.
The whole point of using shamans is to quickly level your wizard. The best skills to choose are necromancy and summoning. If you get both up to rank 3, your zombies will be extremely tanky, having 30+HP! You have to kill a living unit to make it leave a corpse for reanimation, so keep two magic arrows in your spellbook. Imps will do in pinch, but zombies are great damage sponges and skeletons are good archer hunters.
By the time your wizard hits about level 12, if you've got both summoning and necromancy you can quickly defeat all enemy garrisons and siege the enemy stronghold. I've won a few "I'm no coward, but I'd rather retreat" battles because the adviser doesn't take into account your summoning potential.