  We show that breather solutions of the Gardner equation, a natural
generalization of the KdV and mKdV equations, are $H^2(\mathbb{R})$ stable.
Through a variational approach, we characterize Gardner breathers as minimizers
of a new Lyapunov functional and we study the associated spectral problem,
through $(i)$ the analysis of the spectrum of explicit linear systems
(\emph{spectral stability}), and $(ii)$ controlling degenerated directions by
using low regularity conservation laws.
