My son is considering applying for this as well. He has not done so yet, but here are two resources you might find useful:
1. Monbukagakusho Prep. Guide
http://www.graduateinjapan.com/
2. Blog entitled "How I Got the Monbusho Research Scholarship"
http://larsmartinson.com/how-i-got-the-monbusho-research-scholarship-part-1-of-4/
Good luck!