Soldiers
The Geonosian grunts are going to be among the more annoying enemies you face in the game. They're not particularly tough to kill, but their ability to fly and their hard-hitting melee attacks can be difficult to deal with.

In most instances, Geo soldiers will appear en masse and attempt to overwhelm you with sheer numbers, and they're fairly good at doing so, thanks to the fact that they'll usually charge in and hit you with their cudgels. A single blow from a cudgel will usually reduce you to half health or lower on hard mode, making it easy for them to take you out if you don't exercise a great amount of caution. A single melee attack will usually kill them, but their flight abilities can make it difficult to actually hit them until they're already in range for their own melee swings. Their flight also makes Geonosians less susceptible to grenade fire.

Your best bet for taking down soldiers lies in getting a commando into a snipe position; a single sniper round will pop a soldier in two. Unassigned commandos will do a decent job of taking down hostiles with their blaster fire, and can also counterattack the soldier's melee attacks automatically, but if you don't provide adequate cover fire, soldiers will often surround your squadmate and start beating him down, so keep an eye on their health meters during firefights.

Elites
Geonosian Elites, although rare, are incredibly aggravating enemies for a number of reasons, foremost of which is their devastating laser attack. The Elite laser is one of the most powerful weapons in the game, and will rip through your squadmates and yourself if you take it directly; when it's aimed at you, your best bet is to keep moving and get an obstacle or wall between yourself and the Elite. Your squadmates are going to be worse off, though. Even if they're in a position where they have cover, Elites will usually fly above them and fire so that the cover is effectively negated.

Elites are annoying! If you're able to get behind cover, though, feel free to use their own laser weapon against them.

Unfortunately, Elites have boosted health to go along with their powerful attacks, and can withstand multiple sniper shots without dying. That said, sniping is still usually going to be your weapon of choice against these guys, if only because they're even more resistant to most other forms of damage. Since they never touch the ground, anti-armor shells and grenades are mostly useless against them (unless you can stick a sonic detonator to a wall you think they'll fly near), and blaster fire is a bit too weak to really hurt them. Most areas that feature Elites will also feature multiple sniper positions for your teammates, though, so try and get them all into one. Most Elites will take around six sniper shots before going down, so the instakills that you'll have gotten on the soldiers will be a thing of the past, but this is still the most efficient manner of killing them.

Trandoshans

Slaver
Slavers are the Trando equivalent of battle droids: they hunt in packs, but aren't physically very difficult to be rid of. They wield ACP Array Guns, which can be crippling if you let them get in close, but which possess only a small chance of actually hitting anything when fired at anything other than point-blank range. You have to be careful, though, as if you damage them enough, they'll drop their shotguns and switch over to knives, at which point they'll close in on you and attempt to damage you with melee attacks. Still, though, as befitting grunts, most any weapon will kill them without much of a problem. A favorite tactic of ours was to stun groups of them with flashbang grenades before running up and slaughtering the lot with melee attacks to the face, but we're just naughty like that.

Mercenary
Although theoretically military-trained, Trando mercs aren't that much more dangerous than their slaver brethren. While their SMG weapons are capable of putting out a much more constant stream of fire in the air, they're not tremendously damaging, or even very accurate outside of close range. They also can't take much more damage than slavers; they're still instantly killed by a melee attack or a sniper round, for instance, so you shouldn't need to use any special tactics to get kills on these guys.

Although you can't pick mercs up by their legs and crush their ribcages with your bare hands, like this Wookiee, you'll still be able to kill plenty of Trandos over the course of Republic Commando.

On fun aspect of the mercenary is their habit of wearing Boba Fett-ish jetpacks on their backs. Although they regretfully never use them in the game (which would've been pretty awesome), you can still have a little fun with these by shooting them, which will cause the merc to fly up into the air and instantly die. Heck, you can even do this after killing a merc; just shoot the rocket pack on their corpse and watch the fireworks. It never gets old!

Heavily-Armored Mercenary
The Trandoshan HAM is one of the rarest, yet fiercest enemies in the game. These bulky warriors are armored from feet to chest in mostly impenetrable metal, but they do leave one weak spot unexposed: their head. If you can get a clean shot at their head, then you should be able to take them down in three or four sniper hits. The problem, of course, is actually hitting them without getting torn to shreds by their Repeater Guns; these babies can bring you down in no time flat if you're not behind cover. The best opportunity for taking down a HAM is by stunning it with a flashbang grenade; if you can do that, then you should be able to take your time aiming and firing your sniper rifle and finish the beastie off.