Baby I

To get YukimiBotamon:
Born from Egg

Baby II

To get Nyaromon:
Botamon: Wait about 60 Minutes

Child

To get Agumon (R only) or Gaomon (L only):
Nyaromon: -1 Calls

To get Guilmon (R only) or Gabumon (L only):
Nyaromon: 2-3 Calls

To get Gotsumon:
Nyaromon: 4+ Calls

To get Agumon Hakase:
Nyaromon: 0-1 Calls
Must have been born from special event egg.

Adult

To get GeoGreymon (R only):
Agumon: -2 Calls, Train 25+
Agumon Hakase: 0-4 Calls, Train 12-24

To get Gaogamon (L only):
Gaomon: -2 Calls, Train 25+

To get Growmon: (R only):
Agumon: 0-4 Calls, Train 10-24
Guilmon: -2 Calls, Train 25+

To get Garurumon (L only):
Gaomon: 0-4 Calls, Train 12-24
Gabumon: -2 Calls, Train 25+
Agumon Hakase: 0-4 Calls, Train 12-24

To get Flymon:
Gabumon: 0-4 Calls, Train 10-24
Guilmon: 0-4 Calls, Train 10-24
Gotsumon: 0-2 Calls, Train 25+

To get Cockatorimon:
Gotsumon: 0-4 Calls, Train 10-24

To get Veggiemon:
All Child Digimon: When other evolution conditions are not met.

To get Wizarmon:
Agumon Hakase: -1 Calls, Train 25+
Must have been born from the special event egg.

Perfect

To get RiseGreymon (R only):
GeoGreymon: -1 Calls, Perfect Conditions met
Veggiemon: -1 Calls, Perfect Conditions met

To get MachGaogamon (L only):
Gaogamon: -1 Calls, Perfect Conditions met
Veggiemon: -1 Calls, Perfect Conditions met

To get MegaloGrowmon (R only):
Growmon: -1 Calls, Perfect Conditions met

To get WereGarurumon (L only):
Garurumon: -1 Calls, Perfect Conditions met

To get Anomalocarimon:
GeoGreymon, Growmon, Gaogamon, WereGarurumon: 2-3 Calls, Perfect Conditions met
Flymon, Cockatorimon: 0-3 Calls, Perfect Conditions met
Veggiemon: 2-3 Calls, Perfect Conditions met

To get Digitamamon:
From all Adult Digimon: 5 bombs (?)

To get Piccolomon:
Wizarmon: -1 Calls, Perfect Conditions met
Veggiemon: ???
This Digimon must have been born from the special event egg.

Ultimate

To get ShineGreymon (R only):
RiseGreymon: -2 Calls, Perfect Conditions

To get MirageGaogamon (L only):
MachGaogamon: -2 Calls, Perfect Conditions

To get Dukemon (R only):
MegaloGrowmon: -2 Calls, Perfect Conditions

To get MetalGarurumon (L only):
WereGarurumon: -2 Calls, Perfect Conditions

To get Pinocchimon:
Digitamamon: 0-4 Calls, Perfect Conditions

To get Minervamon:
Digitamamon: 5 Bombs (???)
This Digimon must have been born from the special event egg.

To get VictoryGreymon (R only):
Piccolomon: -1 Calls, Perfect Conditions
This Digimon must have been born from the special event egg.

To get Z'D Garurumon (L only):
Piccolomon: -1 Calls, Perfect Conditions
This Digimon must have been born from the special event egg.

Other

To get Burpmon:
Any Digimon: Weight above 80G. Burpmon cannot battle and will turn other Digimon into Burpmon during Event Communication. Burpmon will return to its previous form when its weight drops.

Perfect Conditions:
20 or more battles. A 40% Win Ratio gives a small chance of evolution, 60% gives a better chance, and 80% and higher gives the best chance. Event Communication is also required for evolution. 10-19 instances of Event Communication gives a small chance, 20-29 instances gives a better chance, and 30 gives the best chance.

Calls:
A Call is when the Digimon cries out for attention and the need is not met within a certain amount of time. On the Twins, this takes twenty minutes, unless the Call is for lights out at bedtime, as then only have five minutes. Note that the Strength meter will drop while the Digimon sleeps, making it important to train right when the Digimon wakes up to avoid a Call; you have twenty minutes after the Digimon wakes up before this counts. Accumulation of poop will not count as a Call.