There are at this time 4 different Major Arkfall types. They are Revolting Hellbugs, Mother of All Hellbugs, Hellbug Uprising, and Scrapper Uprising.
You will know it is a major arkfall because there will be a large red circle on your map with 5 arkfall crystals inside. When you enter the large red circle you will see the name of which type of Major Arkfall it is at the top of your screen. I completed Hellbug Uprising with just 7 of us, and even solo'd an entire Scrapper Uprising one by myself late one night when no one was around in San Fran. They scale in difficulty to the number of players attempting them. That said, the Hellbug ones where you have to destroy the crystals that skitterlings are biting and creating weak points on take forever, so its doubtful one person could solo an entire Major Arkfall containing these for the 5 crystals, though not impossible. Obviously as you and your teammates progress in Ego and have ideal Perk setups for damage output, they become easier.
For each type, destroy the 5 smaller crystals to spawn the "boss". Boss kill methods below:
1. Revolting Hellbugs - Ignore the smaller enemies. Shoot the 3 mouths on the big guy to spawn the Hellbug Hellion flying symbiote and unload on him. He will retreat and one Monarch will spawn. Kill it to have him come back out. Once you damage it and it retreats again TWO Monarchs will come out. After destroying them the last phase of the flying Hellion begins. Down him and you're done.
2. Mother of all Hellbugs - The simplest Major Arkfall, doable with a few solid players or even solo if you're decent at shooters. After destroying the 5 crystals the boss will be a giant fat tick looking Hellbug Matron. Shoot her in the mouth (her weak point) for double damage. Otherwise just unload on her when she surfaces. The only small enemies you want to worry about are the mortar-firing mounds near the end as they are dangerous with infinite range almost.
3. Hellbug Uprising - Your boss here after the 5 crystals looks just like type 1's boss except it has three arms instead of mouths. Shoot the yellow glands under the arms to destroy them forcing the flying Hellbug Hellion symbiote out of hiding. Rinse and repeat for the three arms. Eventually a Monarch (possibly two) will spawn. Kill the Monarch to bring the Hellion back out and finish it off.
4. Scrapper Uprising - After the 5 crystals, this is a giant mechanical boss with four scorpion-like arms that blast you, one at each corner. Ignore the smaller enemies and have one or two players damage the larger "forge" enemies and 'pull' them away from the main fighting group. The rest need to all focus fire on just one or two arms at a time, destroying the 3 yellow Heatsink weak points. Once all four arms are down the center boss will fly around repairing them. When it does, its belly will open exposing its weak point for a VERY short time. It is essential that EVERYONE be shooting at the weak point when it opens. A couple cycles of downing the arms and shooting its belly and victory is yours.