This boss is divided into 3 phases. The first phase is relatively easy. However the second phase is extremely RNG dependent and the difficulty of the third phase relies on how second phase turned out.
Adds will spawn one at a time from the green clouds on the first phase. These adds don't do too much damage and can be easily killed. The aim is to kill the adds near Sara so that she can take damage when the boss explodes upon death. Care must be taken not to walk into the clouds as that will trigger additional spawns. Kill 8 adds near Sara to trigger into phase 2.
Phase 2 begins with the appearance of Yogg-Saron himself, although surrounded by a shield that makes him immune to everything. At the same time tentacles will appear that needs to be killed. There are three types of tentacles that will appear and the priority to kill them is Constrictor, Corruptor and lastly Crusher. The main hindrance in this phase comes from the corruptor tentacles and these needs to be killed within10 seconds after spawn or else the ability to kill the crusher tentacles on time is severed jeopardized, leading to inevitable wipes on phase 3. This is where RNG comes into play. Since the spawn locations of these tentacles are random around the room, good RNG means the spawn location of corruptor and crusher tentacles are nearby and within reach without much movement. This allows them to be nuked down on time or even ahead of time. Around 1 minute or so into this phase, portals open up into Yogg's brain and that must be burned down to 30% in one passing (or else its another wipe on p3) to trigger phase 3.
Phase 3 starts when the brain reaches 30%. Any tentacles left in phase 2 will undoubtedly become a hindrance and hence must be burned down fast. This is why it is a good idea to kill at least all the corruptor tentacles in phase 2. When phase 3 starts, Yogg will become attackable and has just over 3 million health. The difficult part of this phase is that an Immortal guardian will spawn every 10-15 sec and these will need to be burned down before the next one spawns. It is preferable to kill them with at least 4 seconds to spare so that there is time to refresh DoTs on Yogg or do a double SWD.