Engaging the Enemy (Apocalypse)
When entering the battlescape, it is always best to use real time, except when going for a capture. The tactics you employ may vary widely depending on who you face, but are vastly different from those employed in the first two games. This is divided into early, middle, and late game vs. both aliens and other humans.
The Difference
The main difference is in the availability of armor in the early game. Megapol and even Marsec armor is nearly immune to early-game weaponry, a far cry from the instant death plasma of the first game. Only hyperworms can easily penetrate this armor until the boomeroid is deployed.
Early Game: Aliens
At first, your only real worries are multiworms/hyperworms and brainsuckers, though spitters are dangerous in large numbers. Multiworms themselves are not dangerous outside of very short range (their acid spit can take chunks out of an unlucky stun squadder's health though), but it's hard to kill them at range and hyperworms are death in melee. Use autocannons and machine guns, preferably two weapons per trooper, then upgrade to plasma guns as soon as you can. Grenades are only slightly effective, as they are often unable to kill in a single hit or noticeably weaken enemies, though a well-timed Megapol AP Grenade can kill the Hyperworms as they burst from their deceased parent. Stun gas, however, is pretty useful for captures and beating multiworms. Missile launchers have a large blast radius, making it easy to hit your troops at times and often inflicting a fair amount of collateral damage, so it's best to not rely on them.
Early Game: Humans
This varies widely, as the different groups are armed differently, but what you really have to worry about are cultists, gang members, Marsec troops, and Megapol, as these are the most dangerous.
Cultists wear Megapol armor, and have autocannons, grenades, plasma guns, rocket launchers, and basically everything Megapol sells.
Gang members are equipped with a wide array of guns, though plasma guns are somewhat rare. Diablo members are equipped with incendiary grenades on occasion.
Marsec troops have Marsec gear.
Megapol troops have Megapol's inventory of lethal weaponry.
In all cases your main advantage is that you can employ grenades frequently. Explosive autocannon fire is also of great value, as your enemies tend to clump. Target rocket launchers first, then shoot whoever is shooting at you. Inflict maximum collateral damage, as a bankrupted foe can't counterattack.
Mid Game: Aliens
When you pass 1000 points, things take a change for the lethal. The arthropods are now the prime target, behind only charging brainsuckers and poppers in threat. Claiming disruptor guns slightly evens the odds, but your armor advantage is long gone. Skeletoids start to appear, and the nightmare of storming UFOs is not much changed from the other two games; if anything, it is now even more dangerous. When boomeroids appear, things get even worse, though the non-armed aliens are now easy meat for disruptor guns. Eventually the devastator cannon is deployed, proving lethal to even armored androids in as few as two shots at times. Begin phasing out human weaponry as fast as possible and keep your troops far apart when you can.
Mid Game: Humans
This is much easier, as you are now equipped with the most lethal weaponry. In almost any battle, X-COM troops should shred any resistance, though you must still be wary of rocket launchers and plasma guns.
Late Game: Humans
By this point, humans will usually be complete pushovers. Protected by X-Com disruptor armor and personal shields, even taking direct hits from rocket launchers will do little to slow your agents down, and with devastator cannons and dimension missile launchers, you'll make short work of whatever human enemies try to take you out.
Storming UFOs
This can be tough, even early on. Early in the game, you'll start facing your first manned alien craft: transports and fast attack ships. Most of these follow the same basic design, a central gravity lift with the ship's control center on the upper floor. Ship entrances can vary significantly; transports have two exits on opposite sides of the craft for example, whilst others have only a single exit. Agent positioning at the start of the battle can mean the difference between a turkey shoot and a chaotic fight on open terrain.
A good - though slow - tactic is to position your agents in a rough half-circle or quarter-circle around the exit door(s) at around a dozen squares away as terrain permits and wait for the aliens to come to you, rather than wading into a deathtrap. Snipers can be further; less accurate troops or those using grenades should be closer. Do not bunch up - grenades ruin your day as much as they ruin the alien's', and the monstrous Megaspawn has a very powerful missile launcher you do not want to be hit by.
Cover outside tends to be sparse so make the most of dips or rises in the terrain for height advantage/hard cover, and use trees/bushes as 'soft' cover. Only if the aliens refuse to leave their camping spots should you risk venturing inside - if the aliens haven't left the craft yet, you'll run into a few of them as soon as you enter the ship's hallway. Be careful not to get bunched up entering or a well-placed boomeroid can cause some serious harm to your troops.
Eventually, you'll want to secure the bottom of the lift, then move upward to the control center. One useful technique, if you can pull off the throw, is to lob a smoke or gas grenade up onto the upper floor from below. Smoke will help you move your agents into position without coming under fire, while gas grenades will ensure that there are no aliens (especially brainsuckers) lying in wait right at the top of the lift.
Once you enter the control room, be prepared for a real fight. Unless you were met by a large number of alien attackers in the entryway, the bulk of the ship's crew is likely to be up on this level, and most of the time they're entrenched behind barricades or up on elevated catwalks, giving them a tactical advantage. Making use of gas grenades here to flush aliens out of their cover can greatly improve your odds of coming away without casualties.
It's important not to get complacent. Even late in the game, when you're wearing the best armor and toting devistators and shields, alien incursions in buildings can seem like cake, but UFO crews will almost always be as well-armed as you are and will have the tactical advantage in many cases.
Tactics for human buildings
X-COM Base
See Base Defense (Apocalypse) for more info.
The layout is of course dependent on how you've designed your base, so make sure you use Security Stations! Pull your civilian personnel into a safer part of the installation with a squad to guard them, then start sweeping for any intruders that might have escaped your security net.
Temples of Sirius
All indoors, with fairly large open rooms split apart by thin walls with double doors at the corners, and small, tunnel-filled basements or small offices on the lowest level. Unpleasant to fight in but far from the worst terrain. Rows of pews and low walls offer plenty of 'soft' cover from small arms fire, while many pillars and the occasional altar present harder full cover that can absorb one or more Devastator shots.
Walls are thin and easily breached if you want to make your own doors.
Corporate Headquarters
The corporate headquarters are almost the closest thing you'll get to an open-field battle in any of the maps in Mega-Primus. Be glad, because they're also the alien's preferred target. There are three major layouts.
First and most common is a single solid building with a large lobby, with a gravlift and a horde of aliens in it. Enter the lobby with all your troops at once and gun down the aliens inside. Other aliens will swarm down the gravlift and out the nearby doors, so most aliens will be involved.
After that, hunt the rest down with squads of troops; they prefer hiding upstairs.
Second, there's a pathway with small towers lining it. Most aliens will emerge onto the pathway and can be cut down by mass fire. Again, hunt down the survivors in the towers afterwards.
Last but not least there is a sprawling building with numerous entry points. Sadly, there is no area that the aliens will reliably swarm towards when you open fire.
Slum
The slum is either an obstructed field, a brutal room to room hunt for aliens in some large buildings, another obstructed field with small buildings, or a building wrapped around a clear area, which you need to get cleared of enemies while dealing with enemies on the balconies. The building missions tend to have some mostly empty levels and some levels filled with enemies. The field missions... you remember the farm and forest terrain from X-com1? kinda like that, with more trees.
Be on the lookout for supported structures like the water tanks. They are fairly lightly supported and stray fire could easily bring them down on top of your men.
Apartments
These are all small rooms with open common areas and fairly long hallways, ideal for being ambushed and separated... in other words, these suck. On the other hand they offer decent flanking opportunities to offset their many bottlenecks; if an enemy has you pinned down in a corridor (or vice versa) there is generally a good way to flank them nearby, and smoke grenades can be used to make things a little easier.
Cover is pretty sparse, but columns here and there offer fairly good protection from small arms and you only ever need to cover a single floor. Agents can also duck into the apartments if you're setting up an ambush, or to recover from their injuries using a Medi-Kit. Eggs and Chrysalis' may often be found tucked in bathrooms.
Megapol Stations
If you thought Apartments were bad, these are a hundred times worse. Extremely tight corridors with many small rooms and an abundance of doorways. Do not go into battle in one of these unless you are exceptionally well-prepared and armed with end-game tier equipment like shields, alien weapons, and manufactured armour, unless it is the early game and aliens are not packing lethal ranged weapons. Motion sensors are useful.