What if I know for sure that my target variable is not normally but Beta distributed? As stated in the question, what sort of modeling technique would be most appropriate? 
 A: beta regression: see Fransisco Cribari-Neto and Achim Zeileis, "Beta Regression in R", Journal of Statistical Software, volume 34, issue 2, April 2010.  If you have linear regression problem with a Beta noise process, then this is the neat solution.
A: In addition to the suggestions, you could also try the logit transformation:
$$\log \frac{p}{1-p}$$
where $p$ is a Beta random variable.
You can now fit a linear regression model. The estimates would be ok, the only thing that might be a problem are inferences regarding the regression coefficients.
In order to avoid this problem, I would choose Bayesian approaches that impose a diffuse t-prior on the regression coefficients. If you don't have a huge data set, you could try either the bayesglm function in the arm package or fit a hierarchical model using JAGS and rjags package in R. Otherwise if you have a huge data set, normal Gaussian regression should work fine.
However, I must remark that the choice depends on the specific data that you have and the interpretation of the parameter estimates.   
