It’s been a while since I played Final Fight, but I remember laying down a couple of early Line Lasers to cover both paths. They deal with low health enemies nicely, allowing you to build up a nest egg for later construction. Once I lose my two barriers I start building up defences around the final gate (e.g. beams+booster on the grey 3×3 square) where they can reach incoming critters from the left hand entrance too. If necessary, sell off any inefficient towers on the right side of the map to fund this.
Let us know how you get on 