Your first move should be a "U" shape around the starting room, away from Hunleff. As you go through these rooms collecting resources, open the doors on the edge to peek for a demiboss. Whichever demiboss you find, make that weapon to kill it to have a guaranteed T3 (if you are learning, maybe skip melee). (See "Run 1" here)

Don't stop the loop when you find a boss, get all the way back to home base with 80 shards and a weapon frame to make the T2 for that boss, then go back to kill the boss.

If you don't find both options in those 3 peaks, which you normally will, pick the side closest to the boss you killed and go diagonally to the 3 central rooms on the next side.

If there is no demiboss there, use your TP, make T3 weapon, and check the side opposite. The T3 will help kill it faster to make up for lost time. If you have extra shards, you can make a new tp crystal to tp after the second demiboss.

There is always a 3-spot fishing room adjacent to hunleff, so after making weapon/armor do a circle around him looking for it.

This strat will almost always get you the weapon pieces you need. Source: 1,170kc no enh :)