If you have like 70 or so it may one day be possible to purchase (real money) or maybe even win (tournaments) the needed fragments.  For the most part I've never completed a frag champ after the event.

but champs from doom tower and other content are different.  You accumulate these slowly and will eventually get the frags you need,

Thanks for the information, I'm not far off from the doom tower champion on normal also about the same from the Bizzare.

Some of the champs I've got fragments for I've since pulled in shards just seems a waste. Pity that twice a year you can't pool them altogether to obtain something useful.

There have been, I believe, three different Fragment Top Up events over the past couple years. This is where they pick a half dozen fusions or so and have special Dragon Tourneys, or Champ Training Events, etc, for you to earn small amounts of fragments for previous fragment fusion champs.

I think the most I have seen available was 20 or 25 per champ, and that is IF you did the events AND *won* the tourneys. And I think in at least one of those times they sold frags at the end to finish out champs if you wanted?

Anyways, I have used this process to finish up a fusion I didn't finish from a while ago by dropping a decent amount of gems to secure some tourney wins. :D