Once Bergmann activates the Bio-Domes you will have to run around Apollo and fight various types of enemies at a series of domes. These occur in random order, but D will always be last, as it must be destroyed. Most teams will press the domes, causing enemies to come from a single directing, and freeing the city for a Recon to rescue civilians. Alternatively you can flee to a defensible location and have an Operations Commando simply Nuke the domes and eliminate most of the enemies, letting the rest come to you.
Dome A consists only of zombies, and is generally the easiest. It may contain zombies, Immortals, and Infested Marines, and will mainly try to simply overwhelm you. High aoe skills and high splash weapons are recommended. Tanks will have little problem chewing through enemies also.
Dome B consists of Gargoyles, Stranglers, and on higher difficulties, Wraiths. It is best to keep enemies at bay with Sonic Traps; these will also keep Stranglers from hugging players. Once again, high splash weapons and aoe skills work great, but lasers or high damage single target skills like One Shot One Kill are needed to dispense the Stranglers, as they have very high armor.
Dome C consists of heavily armored enemies and banelings. It is mostly Agrons, Stalkers, and Banelings, with Devourers entering the fray on higher difficulties as well as a chance of Beastlings spawning which increases with difficulty. This dome should be considered untankable, even with Reactive Armor the enemies can wear down a tank, and stack many many injuries. It is best to unload on this dome, using the strongest weapons and skills. Sonic Traps won't necessarily hold back enemies here as they do other domes, but they will keep the banelings at bay.
Dome D is the only Dome that must physically be destroyed. It will spawn a collection of virtually every type of infested, including the powerful Slasher on higher difficulties. It should also be put down with gratuitous amounts of firepower. Once the dome is vulnerable, OSOK, Nukes, and high damage weapons ensure it dies quickly.
Once the Bio-Domes are cleared, your team can prepare to deal with the real threat.