|(This is an edit from my previous build) Barst is an under appreciated axe unit, seeing how he's outclassed by a lot of other axe units in the game. However, he still has a place for me and for other Barst lovers out there!
Barst has an offensive spread of 33/32 which is serviceable. For this build, you want a +SPD Barst, -RES is unfortunately his mega bane, so if arena scoring is important to you, then the next best bane is -HP. Because his RES is pitifully low, he is not meant to be in the range of any mage or dragon. Although his HP is high enough to tank a single hit, I would not bank on it.
His weapon of choice his the Giant Spoon+, this Wo Dao axe is absolutely perfect when combined with Wrath, he's get an additional +20 to his special if the conditions are met. If you do not have access to the spoon though, Slaying Axe works just as well. For his special, Glimmer is his best option (although Moonbow is also a viable option if you frequently run into high defense units). Bonfire is another solid choice since he has pretty good DEF, especially if you run Slaying Axe with him. As for the refine, SPD is the better option for him.
Fury is always a good skill, it'll bump up his speed even higher, as well as his other stats. Not only that, but because of the damage he'll be getting from Fury and from combat as well, he'll go into the Wrath range quicker. Wrath synergizes incredibly well with Giant Spoon+. +20 additional damage to specials is nothing to scoff at, even without the spoon, a special like Bonfire with an extra +10 damage can still do a scary amount of damage.
For his sacred seal, Speed +3 is highly recommended. With this seal, a +SPD nature, SPD refine weapon and Fury, Barst can reach 44 SPD unmerged and unboosted! That's a lot of speed for a simple woodcutter. You could also run Quickened Pulse to make his special charges even shorter, making him a very scary axe unit.