Using Daggers against MOOSTAFA is a risky bet, as it has the lowest range of any weapon, along with the Tool Hammer.
However, if you rush in, land a few hits, then go out, you can do theoretically infinite damage without taking any, if you get the timing right.
Also, each attack it does will only cost you a single Cookie, so being hit isn't too bad.
The Polearm and the Bat are less effective, due to their low DPS.
They are very effective, however, for herding MOOSTAFA into one location, due to their powerful knockback.
With the Polearm, you can go to the MOOSTAFA's arena and hit him through the stone when he can't hit you. The Katana can also do this.
Try taking it down in teams. Always have at least one partner, to be cautious.
Or if you are skilled enough, you can simply just solo it.
Keep enemies away from MOOSTAFA. Don't let them steal your kill.
Stay away from MOOSTAFA's giant axe. A good way to do this is with a Ranged Weapon, though these do tend to be weaker and make you slower.
When MOOSTAFA is preparing to attack, it will rapidly rotate to take aim, pause for a short time, then charge at its target while swinging its axe. Learn these signs so that you can dodge his attacks.
The easiest way to beat MOOSTAFA is to get a cactus between you and it. MOOSTAFA will repeatedly run into it, and when MOOSTAFA's health is low enough, you can finish it off with your own weapon.
Another way to beat MOOSTAFA, especially when there are no nearby cacti, is to get it at a mine and hit it with a long range weapon while avoiding its rushes and maneuvering around the mine to keep MOOSTAFA approximately opposite from you.
Try leading MOOSTAFA into the entrance to the arena. At some angles, you can hit him with a sword but he can't hit you.
To get him into the entrance, use Walls to push him back. Alternatively, you can use Spikes, as they have powerful knockback, but will be damaged by contact.
When Sidney de Vries first announced MOOSTAFA, he put him next to a Treasure Chest. This Treasure Chest appeared in game one update after version 1.0.
This mob has the best AI in the game but is extremely slow.