For the longest time, I thought this achievement was bugged and unobtainable since I did exactly what it said to do and I wasn't getting the achievement. I thought I tried everything to get this achievement. I even sent an email to the developers asking about it and they told me they weren't working on this game anymore and couldn't help.

I eventually figured out what to do by piecing together information from other guides and comments, so hopefully this helps out others in need of some assistance.

Initially, I played through the game and completed every level without using any abilities, making sure I showed up on the leader board for every level marked as having used no abilities. After doing that, I didn't earn the achievement, so I thought the final level was bugged since the leader board for 9-10 doesn't show anything for me.

After giving up on this for a while, I decided to come back and see if I could try something else to earn this. I found some people suggesting that I complete the last level of every world without abilities, so I did that and still didn't get the achievement. I then decided to try also completing level 9-9 since that was the last level to have a functional leader board. Once I did that, I earned the achievement.

During my initial play-through, I ended up buying all of the abilities anyway and I've seen some people say that this is an important thing to do for this achievement, so I thought I'd mention it here.

Quick list of how I earned this achievement:

• Complete every level in the game without abilities (possibly not necessary, but I'm not sure)
  
• Purchase all abilities but still don't equip any (possibly not necessary, but I'm not sure)
  
• Complete the last level in each world with no abilities equipped
  
• Complete level 9-9 with no abilities equipped

Most of the info I got for this was found here in the guide and a lot of comments: https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=1371170493