It's been forever since I played, but I definitely remember it being a tricky stage due to layout and bomb jumping. I did find this video on it:
https://www.youtube.com/watch?v=rOdy53FHGWs
Gold card at 1:10. The trick they use is probably easier than trying to jump across and back normally. If you find it difficult you can make the last bomb in the jump chain a pumped bomb to make sure you get the height you need.
After that, switch to this video (use the seams between the ground cubes as a visual ruler to line up your bomb throws and placements):
https://www.youtube.com/watch?v=ye7ca8vglR0
General advice, it looks like slightly lower flame sizes are preferable since they give you more room to avoid blowing yourself up. The cloud enemies can be baited to fire early, and you can initiate a bomb jump from ground level by tossing a bomb against a wall, knocking yourself out and back onto a bomb.
Hopefully this gives you some help. Good luck.