Classically, you should use its non parametric equivalent (kruskal wallis). I don't know whether kruskal wallis support taking interaction (two way) or not.

Since ANOVA is a general linear model (LM), you can perform a non generalized linear regression and check its R2. If it was OK, you can report your LM results as both regression approach and ANCOVA approach.

If you are using R software, you can perform ANOVA (ANCOVA) as the post estimation of an LM having regression approach.

Rescale the response to (0, 1) and use a mixed beta regression model. Or inverse logit transform the rescaled values and use a mixed linear model. If you are more interested in estimating the expected values (rather then effects), better use the beta model. The effect estimates should be the same in both cases.

Dear José Luis Palazón F ,

Kruskal-Wallis only works with one way ANOVA. The homogeneity of variance condition is more important than the normality. There are research studies into the robust use of two way ANOVA with non-normal data. It is the normality of the errors that matters, not the normality of the dependent variables. Shapiro-Wilk is a more sensitive normality test than KS.

You can use the kruskal wallis test