There are 25 Chalice Dungeons, half of them fixed, the other half random dungeons. Their difficulty varies (and it's not affected by successive playthroughs of the main story), some are easy but some are quite challenging. You can also make the dungeons harder by adding different materials to the ritual, increasing the worth of the booty.
By far, the hardest dungeon you'll have to clear in your path to the platinum trophy is the defiled one that you'll have to beat with half your life bar
I've beaten 8-10 Chalices so far, all by my own. So yeah, it can be done. I'd like to beat the ones I'm missing cos I've had not too much luck getting rare runes and blood gems so far :/