okay do this, I just tested it out on Adray @ lvl 18 with a defualt attack of 70 & it boosted him to an attack of 9999 (highest in the game)
go back to gemity (the town before sphere with all the games & bullshit) purchase a laser weapon. (equip it if it'll boost your stats any at this point, but don't modify it at all)
go to the arena & play single battle with fayt on S class. you should be able to build up a full bonus guage & start a chain fairly quickly with triple XP & double fol. (even when you lose in the arena you still keep your chain)
complete S class.
a few tips for the single s class battles: the first 3 fights are easily won with the Long O, Short O, Short X, Short X combo.
4th fight is annoying piece of shit chimera. however most of his attacks are AAA'able. so set your AAA to stun. once chimera is stunned, combo that with your most powerfull attack. repeat & he should go down after a few minutes.
5th fight is some huge ape looking things that is a pain in the ass. so use this method: stun bomb, strongest single hit attack, run away, repeat. WATCH OUT FOR HIS ICE BEAM. if you get cuaght by that then the fight is over. if you have any anti/null ice accessories I suggest you use them.
after you finish the single battle mode on s type you will be awarded then imposing scroll.
now go to a workshop. (you can teleport to one through archives)
synth on the imposing scroll to the laser weapon to give it a +1000 ATK factor. next refine the laser weapon five times. (smith/specify plan/laser weapon R#) this will now give the laser weapon a factor of +6000 ATK.
next you need to create some boots of poweress. so take your inventors with the highest levels in crafting (the lil floating fairy bitch works well, I forgot her name) & make some. (craft/original invention w/cost of 2300-2500*/start line)
*you might have to press X on original invention quite a few times before the right cost comes up.
once you have invented a pair, make another. after you have 2 pairs refine both of them twice. (craft/specify plan/boots of poweress) this will take their ATK/DEF +5% attribute & flip it into ATK/DEF +30%.
synth 1 pair of the refined boots of poweress onto the laser weapon. this will give the laser weapon a +6000 ATK, + 30% ATK/DEF factor. equip it to Fayt (or wichever charachtor you use the most) then equip the other pair of refined boots of poweress to his accessory slot. this will sky rocket his attack to 9999 & improve defense a shitload as well.
once his base attack has improved over a few levels he should be at 9999 ATK without the 2nd pair of refined boots equiped. therefore you can aslo synth another factor onto your laser weapon.
BTW, this will cost you around 1,000,000 fol to do. but after a few battles at the arena you'll have that in no time.