// С помощью GetClipboardData(CF_BITMAP) получаю HBITMAP.

function SaveAsPNG(const FileName: WideString; Bitmap: HBITMAP): Boolean;
var
 GPBitmap: TGPBitmap;
 Quality: DWORD;
 EncoderParams: EncoderParameters;
begin
 Result := False;

 GPBitmap := TGPBitmap.Create(Bitmap, 0);
 try
   Quality := 100;

   EncoderParams.Count := 1;
   with EncoderParams.Parameter[0] do
   begin
     Guid           := EncoderQuality;
     NumberOfValues := 1;
     Type_          := EncoderParameterValueTypeLong;
     Value          := @Quality;
   end;

   Result := GPBitmap.Save(FileName, GIUD_Encoder_PNG, @EncoderParams) = Ok;
 finally
   GPBitmap.Free;
 end;
end;

procedure TForm1.FormPaint(Sender: TObject);
var
 DIB: THandle;
 BI: PBitmapInfo;
 Bits: Pointer;
 Bitmap: TGPBitmap;
 Graphics: TGPGraphics;
begin
 if (not IsClipboardFormatAvailable(CF_DIB)) then
   Exit;

 DIB := 0;
 if (OpenClipboard(0)) then
 begin
   DIB := GetClipboardData(CF_DIB);
   CloseClipboard;
 end;

 if (DIB = 0) then
   Exit;

 BI := GlobalLock(DIB);
 Bits := Pointer(Integer(BI) + SizeOf(BI^));

 Graphics := TGPGraphics.Create(Canvas.Handle);
 Bitmap := TGPBitmap.Create(BI^.bmiHeader.biWidth, BI^.bmiHeader.biHeight, BI^.bmiHeader.biWidth * 4, PixelFormat32bppARGB, Bits);
 try
   Graphics.DrawImage(Bitmap, 0, 0);
 finally
   Graphics.Free;
   Bitmap.Free;
 end;

 GlobalUnlock(DIB);
end;