Shrink logs in between user transaction in SQL Server

I have a database where there are like billions of rows and I need to delete the data based on some condition.

Initially I was trying to delete the code in one transaction and log starts growing to the hard disk and fails, then I tried to do it in chunks.

SET NOCOUNT ON;

DECLARE @r INT;

SET @r = 1;

WHILE @r > 0
BEGIN
  BEGIN TRANSACTION;

  DELETE TOP (2000000) -- this will change
    Databasename.dbo.Tablename
    WHERE loading_time < '08/27/2014 4:00:00' 

  SET @r = @@ROWCOUNT;

  COMMIT TRANSACTION;
 -- printing if transaction is commited 
  print 'done'
-- shrinking file after transaction is comminted
  DBCC SHRINKFILE (2, TRUNCATEONLY); -- CHECKPOINT;    -- if simple
  -- BACKUP LOG ... -- if full
END

Is this the right way to delete data and delete logs, in between user transaction because when I did it I get an error ;

Cannot perform a shrinkfile operation inside a user transaction. Terminate the transaction and reissue the statement.