Sounds like a job for structural equation modeling. Changes can be modeled as latent variables, used to predict one another, and lined up in a chain as you've described. For an introduction to latent change modeling, see McArdle (2009); it's quite readable and thorough. Given three latent change variables, you can use one to predict the next, and that next to predict the last. That's a fairly simple structural equation model, and is effectively a fully mediated regression model of the first change predicting the last. You may also want to test for an unmediated predictive relationship between self-esteem change and quality of life change. It shouldn't be hard to find a basic introduction to mediated regression path models, but if it is, you can ask a new question about that (if there isn't one out there already).
McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual Review of Psychology, 60, 577–605.