How to find the attribute that most impacts target variable when multicollinearity is present

regression

#1

When there is multicollinearity between independent variables, we usually do PCA or factor analysis to compress or reduce the dimensions of the data as I know.
But if we want to know the attribute which impacts the target variable more when multicollinearity is present between independent variables, how do we find and what the procedure.
One suggestion was to do regression separately for each independent variable but incase if there are lot of variables how do we do.


#2

First build a Regression model using all attributes, then check for multicollinearity and remove attributes respectively. Then again build model. Check which of the two is working perfectly.