Use the time limited special events to get catalysts to rank up your characters. To start a special event, tap on the "Special Events" tab and choose one of the main three events. You must fully complete the event to get catalysts and other rewards. You have to start the event again if all your champions get knocked out. Additionally, there is a time limited daily event which offers the chance of obtaining special catalysts. For example, the Skill Strike Event will reward you with Skill Catalysts. The Proving Grounds give you all three tiers of basic Catalysts.