Psycho Shift is learned by 8 species by level and 6 by egg

Effect, in PokéAPI's words

“Transfers the user’s major status effect to the target.”

Who learns it

14 species in all, 8 of 11 games shown

Brilliant Diamond and Shining Pearl: 11 species

Species	Method	Level
Hoothoot	Level up	15
Noctowl	Level up	15
Cresselia	Level up	24
Natu	Level up	26
Xatu	Level up	28
Latias	Level up	75
Latios	Level up	75
Abra	Egg
Togepi	Egg
Murkrow	Egg
Spinda	Egg

Sword and Shield: 10 species

Species	Method	Level
Hoothoot	Level up	15
Noctowl	Level up	15
Cresselia	Level up	24
Natu	Level up	26
Xatu	Level up	28
Latias	Level up	75
Latios	Level up	75
Togepi	Egg
Woobat	Egg
Sigilyph	Egg

Ultra Sun and Ultra Moon: 14 species

Species	Method	Level
Cresselia	Level up	1, 75
Hoothoot	Level up	19
Noctowl	Level up	19
Latias	Level up	28
Latios	Level up	28
Natu	Level up	39
Xatu	Level up	43
Deoxys	Level up	43
Abra	Egg
Togepi	Egg
Murkrow	Egg
Spinda	Egg
Woobat	Egg
Sigilyph	Egg

Sun and Moon: 14 species

Species	Method	Level
Cresselia	Level up	1, 75
Hoothoot	Level up	19
Noctowl	Level up	19
Latias	Level up	28
Latios	Level up	28
Natu	Level up	39
Xatu	Level up	43
Deoxys	Level up	43
Abra	Egg
Togepi	Egg
Murkrow	Egg
Spinda	Egg
Woobat	Egg
Sigilyph	Egg

Omega Ruby and Alpha Sapphire: 14 species

Species	Method	Level
Cresselia	Level up	1, 75
Latias	Level up	28
Latios	Level up	28
Natu	Level up	39
Xatu	Level up	43
Deoxys	Level up	43
Hoothoot	Level up	49
Noctowl	Level up	57
Abra	Egg
Togepi	Egg
Murkrow	Egg
Spinda	Egg
Woobat	Egg
Sigilyph	Egg

X and Y: 14 species

Species	Method	Level
Cresselia	Level up	1, 75
Natu	Level up	33
Xatu	Level up	37
Hoothoot	Level up	49
Latias	Level up	50
Latios	Level up	50
Noctowl	Level up	57
Deoxys	Level up	57
Abra	Egg
Togepi	Egg
Murkrow	Egg
Spinda	Egg
Woobat	Egg
Sigilyph	Egg

Black 2 and White 2: 11 species

Species	Method	Level
Natu	Level up	33
Xatu	Level up	37
Hoothoot	Level up	49
Latias	Level up	50
Latios	Level up	50
Noctowl	Level up	57
Deoxys	Level up	57
Cresselia	Level up	75
Togepi	Egg
Murkrow	Egg
Sigilyph	Egg

Black and White: 11 species

Species	Method	Level
Natu	Level up	33
Xatu	Level up	37
Hoothoot	Level up	49
Latias	Level up	50
Latios	Level up	50
Noctowl	Level up	57
Deoxys	Level up	57
Cresselia	Level up	75
Togepi	Egg
Murkrow	Egg
Sigilyph	Egg

Changed over time

One change since Generation IV

1. Through Gen VAccuracy 90%100% from X and Y, Generation VI