Combat varies tremendously, with Caddoc's melee style and E'lara's ranged style. You'll also have a different experience whether you fight through the game in solo mode or team up and tackle it in co-op mode.
Caddoc
Caddoc generally plows into battle to smash in the enemy's face up close and personal. Since Caddoc's main weapons are melee, you want to get close to deal your better damage, though that doesn't mean you always rush in and take a dozen arrows to the chest. Learn how to use cover spots to bounce from safety to safety as you approach your target, and get a feel for when it's better to charge into combat than hang back. You can rely on the crossbow once in a while, but know that it's slow to reload and should always be ready to sprint or Dash to the closest target when the opportunity arises.
A big part of Caddoc's arsenal revolves around Fury. Successful blocks and chained attacks fill up his Fury meter (top left corner of your screen). Unleash a heavy attack when the Fury meter is full and you slam the enemy with a devastating blow. However, the Fury meter depletes over time, so take advantage of the power before it drains away. Also, search out a melee weapon that fills up Fury quickly, and once you open up your second inventory slot, add a second powerful weapon that you can switch to when facing more challenging foes.
Against multiple opponents, don't get swarmed. If the enemy presses in, concentrate your attack on a single foe, wipe it out with a Fury attack or an enchanted weapon hit, then roll through the new gap and pounce on another foe from behind. Never stand still; that's an invitation to take ranged fire and allow the enemy to zero in on you. Practice staying on the move and striking targets as they cross in front of you. Better to slide out of the way of several strikes than stand your ground for one more blow against your opponent. Of course, when an enemy's Health bar drops into the red, hack away to take them down immediately. Sometimes the best defense is indeed a good offense.
E'lara
Unlike Caddoc, E'lara stays out of hand-to-hand combat unless absolutely necessary. Once a fight begins, duck behind the closest cover spot and zoom in on the most dangerous foes with your bow. If you have time, aim for the targets that Caddoc engages to help put them down quickly, and be on the lookout for your next cover spot to give you a better shot or reach safety if you can't immediately pick up where return fire is coming from.
Bows have three speeds: fast (lines reticle), medium (bracket reticle), and slow (circle reticle). In general, fast bows should be E'lara's weapon of choice. Of course, a new enchanted weapon might be the best option, and once you gain your second inventory slot, you'll want a fast bow in one slot and a heavy damage–dealing bow in the second slot. When you pop up from cover, fast bows allow you to shoot and duck back to safety without too much exposure (unlike slow bows), and if you have mana and want to dip into weapon magic (and you will often!), fast bows trigger your weapon magic quickly.
E'lara's roll gives you incredible flexibility in combat, especially in open areas. Practice rolling backward once or twice when enemies close in, and suddenly you've gone from melee combat to range and can continue to fire off arrows. Never get trapped between melee combatants; use roll or sprint to get away, even if it means forgoing damage. Against quick-moving enemies, such as Minotaur, or teleporting enemies, such as Harridan or Infected Wargar, stay on the move to avoid becoming an easy target. Once you learn to strike foes as you dart back and forth, E'lara becomes a nearly unstoppable beast in combat.
Co-op
You're only as good as your partner in this game. Talents unlock through combined kills, and if this wasn't incentive enough, survival should push you to work with your teammate in the heat of battle. Against fast-moving enemies, such as Arackling Crawlers, hacking away in melee side by side or back-to-back cuts through the enemy ranks faster than taking them on solo. When you gain cover, E'lara does well if she can concentrate on picking off targets from a single cover spot or two, which means Caddoc should watch her back and intercept any melee combatants closing on her position. In boss fights, if the two mercenaries don't combine efforts, you can forget about making it through to the next chapter. Each battle might be slightly different, but the fundamentals remain the same: If you stick to each character's strengths and look to protect your partner over reckless aggression, the battle will eventually be yours. Standard combat tactics aside, you can't even take advantage of the talents Battle Charge or Spell Link without Caddoc and E'lara working together.