Yes. As soon as you can see that you didn't land the last hit for the Boss Equip, just hit the "home" button and close it off. The game will restart at the teleport hub.
But for the life of me I can't get Asuna's stat costume. Specifically the attacking one. How do you get attack support to move up? Managed to get cooperation and switch though.
For Attack bonus, what's recommend is
1. Use partner commands to use sword skills (Look out for Attack-type icon! ONLY PRAISE ATTACK-ICONS!!!)
2. Look out for when your partner say "use sword skill, Kirito!" When you use sword skill, they usually follow up with a sword skill of their own, classified under attack type as well (praise them for this)
3. Joint attacks. (Look out for when partners say, "use sword skill together!" If successful, you will see that both you and your partner will get a cut-in portrait as the two of you pull off a flashy attack), this is under Attack type too. Just look out for the icon.
Should you pull off 1+2, you will find your co-operation stat rising pretty fast indeed.
Don't forget you can talk to your partner to indicate to them how you want them to be..attacking type? Supportive type/ use less sword skills? Heal more? Etc etc)