  In this paper we study the multifractal analysis and large derivations for
singular hyperbolic attractors, including the geometric Lorenz attractors. For
each singular hyperbolic homoclinic class whose periodic orbits are all
homoclinically related and such that the space of ergodic probability measures
is connected, we prove that: (i) level sets associated to continuous
observables are dense in the homoclinic class and satisfy a variational
principle; (ii) irregular sets are either empty or are Baire generic and carry
full topological entropy. The assumptions are satisfied by $C^1$-generic
singular hyperbolic attractors and $C^r$-generic geometric Lorenz attractors
$(r\ge 2)$. Finally we prove level-2 large deviations bounds for weak Gibbs
measures, which provide a large deviations principle in the special case of
Gibbs measures. The main technique we apply is the horseshoe approximation
property.
