Blue Moblins are found all over Hyrule, although they are must abundant in the Akkala province, specifically in the area just west of the Akkala Ancient Tech Lab. They are all over the Tumlea Heights and found on both sides of the Bloodleaf Lake. They appear elsewhere, usually in smaller numbers with other Moblins and Bokoblins. There are a troop of them on the Carok Bridge, that connects the Central Tower and Ridgeland Tower regions of Central Hyrule province. They also appear in the Gerudo province, mostly found just north and northwest of the Wasteland Tower, on the higher elevations.
With a health of 144 HP, they are nearly three times as strong as the base (red) Moblin, but have a little less than half as much health as the Black Moblin. Like the standard Moblin, they will drop Moblin Horns and Moblin Fangs when defeated. However, the blue variation will also occasionally drop Moblin Guts.
In Master Mode, the Blue Moblin become the default Moblin, replacing all of the Red Moblin. In turn, the existing Blue Moblin are all replaced with Black Moblins. World Level increases still apply.
Hyrule Compendium entry of the Blue Moblin.