Emperor Palpatine is a very powerful Sith, who works well with characters of a similar category. Obtaining him is only possible during the rare event named Emperor's Demise, which appears every two months (alternating with Grand Master Yoda) and lasts for a week. The event consists of 7 levels and on each of them you have to use a team composed of Rebels. The first fight requires at least 1 star in each character, the second fight requires 2 stars, etc.
The reward for completing each fight is a specific number of character shards, that are then used to unlock the unit. Important: the activation of Emperor Palpatine is only possible after picking up 145 shards, over the course of 5 fights. Each skirmish can only be completed once, so it is only possible to promote the character to 7 stars after completing all stages. The character acquisition progress is saved, so even if you do not finish all the fights during the event, you can continue unlocking Emperor Palpatine in two months.