Think of a dog with a bone - they'll hold onto it with all their might and refuse to let go, no matter what! That's the kind of spirit that "doggedly" embodies.
Here are some synonyms for "doggedly":
* Persistently
* Tenaciously
* Relentlessly
* Stubbornly
* Resolutely
* Indefatigably
* Unwaveringly
Example:
* "The team doggedly pursued their goal, despite the many setbacks they faced."