If your independent variables are correlated, then most likely the estimates of your model parameters will be correlated.
It means that you can't interpret the individual estimates by themselves. The prediction model is still fine, just the estimates are not easily interpretable.
If, for example, beta1 is estimated to be 3 and beta2 is estimated to be 1, then you canNOT say that a one unit change in x1 results in a 3 unit change in Y, because x1 and x2 are correlated, so when x1 changes by 1 unit, x2 is also changing.
What can be done? Remove one (or more) of the highly correlated X's from the model, and adjust your mindset to use the prediction model without trying to interpret the coefficients.