Well for Northern tower: A lot of the mobs are aspirable so I would look into setting at least mp drainkiss or hammer.
Floor 1
I MGS'd past the RDM's patrolling hallway and sniped the WAR's. If no portal then kill a RDM.
Floor 2
Debated killing them all for item chest because I came here for items but also wanted chip. Probably best to just skip them, just kill the MNK. Really easy, just flash during HF or bind/sleep.
Floor 3
Try your hardest to grab one at a time, little shits like to link because the idiot bard or whm will cast crap. Pretty straight forward, kill the brd/whm for chest.
Floor 4
BLMs are extremely squishy, kill them and skip the bad *** in the middle unless you just want items and not chip (I wouldn't risk time dealing with Astral flow).
Floor 5
Extremely easy, make sure shadows are up for EES or flash is on. Also... don't forget echo drops like I did >.> unless you wanna rely on luck.
Floor 6
Skip the wandering tonberries and go for the stationary ones. BLM is easy but when you get to ninja, pull him back a little to behind the ramp. Little ***can one shot you sometimes even at low hp, killed me at 20% hp left with 2hr. So make sure you are far enough away to reraise safely. Also if no portal after the stationary ones are dead, don't touch the SMNs... go for the THF in the previous room after dealing with NIN.
Floor 7
Sleepga and kill. Try to stay close to the others because the rdms seem to resist sleep duration more than the others so they will run after you and its harder to sleep them all at once when awake. I killed BLM's first and went to the RDMs. They are all aspirable too, I set both aspirs for this floor.