Automatic Speech Recognition (ASR) for low-resource languages remains a challenging task due to limited training data. This paper introduces a comprehensive study exploring the effectiveness of Whisper, a pre-trained ASR model, for Northern Kurdish (Kurmanji) an under-resourced language spoken in the Middle East. We investigate three fine-tuning strategies: vanilla, specific parameters, and additional modules. Using a Northern Kurdish fine-tuning speech corpus containing approximately 68 hours of validated transcribed data, our experiments demonstrate that the additional module fine-tuning strategy significantly improves ASR accuracy on a specialized test set, achieving a Word Error Rate (WER) of 10.5% and Character Error Rate (CER) of 5.7% with Whisper version 3. These results underscore the potential of sophisticated transformer models for low-resource ASR and emphasize the importance of tailored fine-tuning techniques for optimal performance.