Any objective can be abandoned by going up to the objective square next to the "current area objective" square, selecting "See all objectives" and selecting a new objective. However, if you want to restart an event objective, you'll need to pay the event currency again to start the event objective again.

If you need more hearts to continue doing other event objectives, just finish the objective you're on (or abandon it, if you can't beat it) and do some "World's Wake" free plays. You can get event currency while in event objectives, but if you're not making progress in them, it's better to just do normal idol-farming runs to get event currency AS WELL as idols instead of idling in an event area and not getting idols.

Good advice from Animenut; also note that you get event tokens when using the Time Warp items Delorean, Time Turner, and Quantum Leap.