Here are some challenges I can think of. Unless stated otherwise no excessive stat potion farming or save state usage is allowed. Also Miracles aren't allowed unless stated otherwise. The up to 40 sets of potions count as gifts from the Egg Dragon. The stated levels are meant for every party member.
Kureji Lufia:
1) Beat Lizard Man at level 5 or lower
2) Beat Big Catfish at level 10 or lower
- no Eagle Rock allowed
3) Beat Regal Goblin at level 15 or lower
- no casino items allowed
- no blue chest items allowed
4) Beat Camu at level 20 or lower
- no casino items allowed
- no blue chest items allowed
- no Bronze Helm allowed (in case of the difficult version)
5) Beat Tarantula at level 25 or lower
- no casino items allowed
- no blue chest items allowed
- no Bronze Helm allowed (in case of the difficult version)
6) Beat Pierre and Danielle at lower 30 or lower
- no casino items allowed
- no blue chest items allowed
7) Beat Gordovan Gades at level 40 or lower
8) Beat Ancient Tower Gades at level 35 or lower
- no blue chest items allowed
9) Beat the lions within 2 rounds
10) Beat Idura 2 at level 45 or lower
- no blue chest items allowed
- no statues/Goddess Idols allowed
- no rewards allowed from beating Master
11) Beat Idura 3 at level 50 or lower
- no blue chest items allowed
- no rewards allowed from beating Master
12) Beat Devil Flower within 4 rounds
- no rewards allowed from beating Master
13) Beat the soldiers (1st encounter) at level 60 or lower
- no blue chest items allowed
- no statues/Goddess Idols allowed
- no rewards allowed from beating Master
14) Beat the gargoyles at level 70 or lower
- no blue chest items allowed
- no rewards allowed from beating Master
15) Beat Revenge Ghost at level 80 or lower
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
16) Beat the white dragons
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
17) Beat Fire Dragon
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
18) Beat Ghost Ship
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
19) Beat Tank
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
20) Beat Shuman Gades
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
21) Beat Strahda Amon
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
22) Beat a pair of Gold Dragons without surprising them
- a save state before the battle is allowed
- Miracles allowed
- no rewards allowed from beating Master
23) Difficult Version: Beat the Master with the endgame party consisting of Maxim, Selan, Guy and Artea
- a save state before the battle is allowed
- Miracles allowed
- no rewards allowed from beating Master beforehand
24) Difficult Version: Beat the Sinistrals on Doom Island
- farming allowed as long as HP and MP don't exceed 999
- no rewards allowed from beating Master and Egg Dragon
- Miracles allowed
- no save states; not even inbetween the battles
25) Difficult Version: Beat the Egg Dragon
- farming allowed as long as HP and MP don't exceed 999
- Miracles allowed
- no rewards allowed from beating Egg Dragon (obviously^^)
26) Hardcore Version: Beat the Master
- use save states before the battle as much as you wish
- Miracles allowed
27) Hardcore Version: Beat the Master with the endgame party consisting of Maxim, Selan, Guy and Artea
- use save states before the battle as much as you wish
- Miracles allowed
- no rewards allowed from beating Master beforehand
28) Hardcore Version: Beat the Sinistrals on Doom Island
- farming allowed; raise your HP and MP as high as you wish
- Miracles allowed
- no rewards allowed from beating Master and Egg Dragon
- save states allowed, but only between the battles
29) Hardcore Version: Beat the Egg Dragon
- farming allowed; raise your HP and MP as high as you wish
- Miracles allowed
- no rewards allowed from beating Egg Dragon (obviously^^)
- save state allowed after the beginning of the final battle phase
Spekkio Lufia:
30) Beat the Sinistrals at Doom Island at level 40 or lower
- Miracles allowed
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
31) Beat La Puella at level 50 or lower
- Miracles allowed
- no stat potion given from Egg Dragon allowed
32) Beat La Puella and her Pet Dragon
- Miracles allowed
33) Beat La Puella
- Miracles allowed
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
34) Beat the Master with the endgame party consisting of Maxim, Selan, Guy and Artea
- a save state before the battle is allowed
- Miracles allowed
- no rewards allowed from beating Master beforehand
35-42) Beat a (level-based) version of the Egg Dragon
- Miracles allowed
- no blue chest items allowed
- no gifts from Egg Dragon allowed
- no rewards allowed from beating Master and Egg Dragon
43) Beat Amon at Spirit Shrine at level 30 or lower (excluding Artea with level 38)
44) Beat Amon at Spirit Shrine at level 30 or lower (excluding Artea with level 38)
- no item usage allowed
