The first game had a setup where certain levels paired you up with Bulma who had her own AI. If you didn't save beforehand and she dies, you would have to restart from the beginning of the level.
The first game had puzzles that involved using Goku's spinning ability to transfer elements from certain pedestals to other pedestals to open certain doors. Getting hit or touching a wall while doing this forced you to do this over again.
That One Attack: In Origins 1, "Monster Carrot" chases Goku at certain points in his boss fight and if he touches you it results in a One-Hit Kill.
That One Level: Doing the higher levels of the survival tower alone in the sequel. Especially if you do it with Bulma who is not well equipped for tough boss battles.