You can in fact do this with the timer off and it isn't too difficult. I recommend saving your devil trigger for the bosses on waves 20 and 40 to make it easier on yourself. Aside from that just know the enemies and how they react and you will be fine!
Edit: ZippyAdam has confirmed that Super Dante can be used for this achievement! Super Dante is unlocked after completing the game on Dante Must Die mode.