You need more than a team of 60s for hard.

Haven't tried it for a while, but in normal mode I have all 60 stages at 3* complete, but only 3 stages of hard mode at 3* and the 4th stage at 2*. I could maybe make it to stage 10 now with equipment and building upgrades I have done since.

As for challenge mode, I have 57/60 complete.