These are films I need to see again, as they could make it on the "best" list. 

some possible contenders: 

Raging Bull (Martin Scorsese / USA / 1980) 

Gallipoli (Peter Weir / Australia / 1981) 
Reds (Warren Beatty / USA / 1981) 
Sjecas li se, Dolly Bell Do You Remember Dolly Bell? (Yugoslavia / Emir Kusturica / 1981) 

The Draughtsman's Contract (Peter Greenaway / UK / 1982) 
Vincent (Tim Burton / USA / 1982) 

L'argent Money (Robert Bresson / France, Switzerland / 1983) 
The King of Comedy (Martin Scosese / USA / 1983) 

Frankenweenie (Tim Burton / USA / 1984) 
Nineteen Eighty-Four (Michael Radford / UK / 1984) 
Once Upon a Time in America (Sergio Leone / USA, Italy / 1984) 

Witness (Peter Weir / USA / 1985) 

Dao ma zei The Horse Thief (Zhuangzhuang Tian / China / 1986) 
Le rayon vert The Green Ray (Eric Rohmer / France / 1986) 
O Melissokomos The Beekeeper (Theodoros Angelopoulos / Greece, France, Italy / 1986) 

Bicycleran The Cyclist (Mohsen Makhmalbaf / Iran / 1987) 

Chocolat (Claire Denis / France, West Germany, Cameroon / 1988) 
Coming to America (John Landis / USA / 1988) 
Dom za veanje Time of the Gypsies (Emir Kusturica / Yugoslavia, UK, Italy / 1988) 
Drowning by Numbers (Peter Greenaway / UK, Netherlands / 1988) 
Tetsuo The Ironman (Shinya Tsukamoto / Japan / 1988) 
The Last Temptation of Christ (Martin Scorsese / USA / 1988) 

The Little Mermaid (Ron Clements / USA / 1989)