It is possible to sue an employer for unfair dismissal. However, it is worth seeking representation. One of the many services offered by unions is legal protection for matters of labour or social welfare law. If you are a member of a union, you will be provided with a DGB lawyer in the case of a dispute.
If you want to contest a termination, you have to act fast. If your industry branch has a court or board of arbitration (generally at the IHK), you should contact them within three weeks of receiving your termination. After the arbitration board or court has listened to you and your employer, they will try to reach an agreement. If this does not work, they will issue a verdict. If one of the parties does not recognise this suggestion, you can initiate legal proceedings within two weeks.
If there is no arbitration board for your industry branch, you must declare your unfair dismissal case to the courts within three weeks after you have received the termination.