Two major types of strategy are common for obtaining competitive advantages in fashion retailing, those concerned with marketing and public relations and those concerned with the actual products.
In terms of products, you can compete on multiple grounds. By off-shoring and cutting production costs, you could compete on price. At the other end of the market, you could compete on quality and rarity -- using exotic materials and making things by hand to offer unique products to customers. You could also compete for the green or ethical consumer market through sustainable and fair sourcing and manufacturing.
On the side of selling and public relations, you can either use unusual sales channels, use social media in an innovative way, or develop other ways of targeting underserved markets or communities to develop a company niche.