Not to try and one-up xTGE, but I just spent alot of time typing this and feel it can offer a few more useful tips on the solution he gave.
This is achievement for Clearing the Legendary Super Saiyan saga.
After defeating the final boss, you'll receive your first Time Chasm Crystal Shard. Once you leave the area with Trunks, there will be an NPC to the right named Recon with a green question mark over his head. Talk to him and he will give you your second time shard.
The last three time shards can be a bit of a grind but I got the shards easier if I completed all of the hidden requirements and/or finished with an ultimate attack.
Time shard 3 can be found on Parallel Quest #49 "Saiyan Revolt."
Hidden requirements: Win with Nappa and Raditz surviving. Defeat Vegito.
Time shard 4 can be found on PQ #14, #18 and #42.
#14 "Legendary Super Saiyan" hidden requirements: Defeat Krillin before Goku. Defeat Super Saiyan Goku.
#18 "Return of Ginyu Force" hidden requirements: Clear in under five minutes. Defeat Frieze
#42 "Power of a Super Saiyan God" hidden requirements: Clear in under three minutes. Defeat revived Goku.
The fifth and final time shard can be collected from PQ #2, #21 and #32
#2 "Prepare for the Attack of Saiyans" hidden requirements: Clear in under five minutes. Defeat Goku. This is also a good quest to farm for Dragonballs. May as well kill two birds with one stone.
#21 "The Cell Games Begin" hidden requirements: Defeat Piccolo and Goku before Gohan. Win without defeating Cell.
#32 "Super Saiyan Bargain Sale" hidden requirements: Clear in under five minutes. Defeat Super Saiyan 3 Goku.
Once you've collected all of the time shards, return to Trunks and he will give you 4 new battles in the last saga.
The first battle is alongside Bardock and the most difficult of the four. You must defeat 15 of Frieza's henchmen and then Frieza himself, with two full orange bars of health, while his henchmen continue to appear. The difficult thing about this battle is that if Bardock dies, you lose. I went in at level 53 and could never get past Frieza without Bardock dying. I decided a new ultimate move would make a world of difference even though Special Beam Cannon could clear a couple of his henchmen at a time. So I went to PQ#25 "17 and 18 of the Official History" for 17's "Super Electric Strike" ultimate attack. Just as with the time shards, I found that completing the hidden requirements ( Clear with Vegeta and Piccolo suriving, Defeat revived 17 and 18 ) and getting an ultimate finish increased my odds of getting the loot. I finally returned at level 61 with my new move and the battle was a breeze, finished first try. It may help to mention that my hero is equipped with the 4-Star Dragon Ball Costume (head to toe) and "I...I'm a super Elite...!!" Z-soul and, of course, four healing capsules.
Once you've completed the battle, your next three fights with Broly should be fairly simple as long as you remember to bring healing capsule. I only used one on each battle and didn't really need it. Better safe than sorry though. He's immune to stagger just like the God battles with Beerus, Whis and Demigra. I suggest staying back and using your supers and ultimates to finish him off.
Feel free to follow me on the one if you need a partner to help with some of the grinds or have any questions. If I missed something, lemme know and I'll update it as soon as I can.