Here is my try
1. An easy and sure way of recovering dues is to entrust this task to professionals.---It didn't sound weird to my ears.
2. The hard core of *** lawyer's office are its legal advisers.-- be careful about the verbs.
3. Their knowledge, experience and objectivity give them an advantage over the other party at the very beginning of proceedings. I'm thinking about "the other party" Is it a good expression here, meaning those from whom we're trying to get our money back for instance. --- I liked it.
4. The great majority of cases entrusted to us ends up in money recovery without the engagement of the court.
5. If the client expresses his wish, there is a possibility of changing the mode of proceedings i.e. bringing an action at law instantly after the first notice to pay.--I couldn't find anything wrong.
However, it is better for you to wait for the native speakers.