"尽管有极大的困难" can be translated into English as "despite tremendous/immense difficulties" or "even with great/enormous difficulties".
Here are some example sentences for context:
Despite tremendous difficulties, they managed to complete the project on time.
（尽管有极大的困难，他们还是按时完成了项目。）
Even with enormous difficulties ahead, we remain determined to succeed.
（尽管前方有极大的困难，我们仍决心取得成功。）