I am trying to perform a multiple regression in R. However, my dependent variable has the following plot:

Here is a scatterplot matrix with all my variables (WAR is the dependent variable):

I know that I need to perform a transformation on this variable (and possibly the independent variables?) but I am not sure of the exact transformation required. Can someone point me in the right direction? I am happy to provide any additional information about the relationship between the independent and dependent variables.

The diagnostic graphics from my regression look as follows:

EDIT

After transforming the dependent and independent variables using Yeo-Johnson transformations, the diagnostic plots look like this:

If I use a GLM with a log-link, the diagnostic graphics are: