We describe a search-based approach to generating new levels for bullet hell games, which are action games characterized by and requiring avoidance of a very large amount of projectiles. Levels are represented using a domain-specific description language, and search in the space defined by this language is performed by a novel variant of the Map-Elites algorithm which incorporates a feasible-infeasible approach to constraint satisfaction. Simulation-based evaluation is used to gauge the fitness of levels, using an agent based on best-first search. The performance of the agent can be tuned according to the two dimensions of strategy and dexterity, making it possible to search for level configurations that require a specific combination of both. As far as we know, this paper describes the first generator for this game genre, and includes several algorithmic innovations.