I was on level 9 for quite a while, and only reached level 10 once I completed the last stage I had left in scenario mode (last one I completed was nightmare train). After that, Alisa upgraded to level 10 and the achievement unlocked. Bonus was that the achievement of completing scenario mode also unlocked :)
From this I am pretty sure you have to complete scenario mode to fully upgrade Alisa... If anyone has done it quicker, let me know.