This can be done on the first mission, scene 1-0. Just try to get close to an enemy and tap until he dies. If you kill an enemy when he was down it does not interfere with the 10 Combos in a row. Also if you die with Jim, switch to the Rebecca and try to revive Jim and go back on the offensive with your melee kills. When you see the floating robot you can try and hide until your computer kills it or run by it and go for the humans behind it.
This can be done with the help of a teammate, just let him/her bring the enemies to you while you melee each one.