After trying Blossom at this (and throwing in her sisters as alts) I ended up getting really close a couple times. BUT then I died and it brought in Buttercup...
she performed wayyy better.
Buttercup near the same basic.forward combo as Blossom but with a slight bit more dmg and her sig.forward attack combo is a flurry of kicks... that combo did nice work as well. That combo will pop more cubes out of the enemies to build PTE. And as for her PTE fireballs they do more damage (from what I could tell) than Blossom's ice breath.
When I took Buttercup as my main she pulled the whole thing off in less time and with not but a tiny bit of Cheese's health gone.
Only problem is from what I could tell she doesn't have much recovery if you happen to fall off.
...ps - HARD on a game like this should not be THAT hard though.