Go to Battleground of Rufescent Regret on the 86th Floor. Make sure Kirito is at least level 114 (or higher, you might be able to defeat it at lower levels but that's what I recommend). You'll have to battle the level 151 Death Mushroom. Make sure you have a selection of powerful skills, you want to do as much damage as fast as you can. You may also want to make use of monster debuffs and party buffs. When you start the battle wait for the shroom to attack (you might get poisoned but don't panic) and then stun it. It's not necessary to stun it but it'll make the battle easier. And then use your skills to prevent it from attacking. Heal when necessary. Aim for a fast victory. After finishing the battle, your partner should level up. Now exit and re-enter the area to respawn the shroom, and fight it again. Rinse and repeat until your partner reaches your desired level.