id INT UNSIGNED AUTO_INCREMENT NOT NULL  -- make it `BIGINT` if expect > 4 billion
PRIMARY KEY(shift, timestamp, id)  -- In this order
INDEX(id),     -- for AUTO_INCREMENT
INDEX(shift)   -- DROP; it is now redundant with new PK
INDEX(tag_id)  -- get rid of this; it is redundant with the next two
INDEX(tag_id, shift, timestamp)  -- what query is this for?
INDEX(tag_id, timestamp)  -- what query is this for?

CREATE TABLE h_new LIKE historical_data;  -- copy schema
ALTER TABLE  h_new ... -- to get PK, better datatypes, indexes, etc.
RENAME TABLE historical_data TO h_old,
             h_new TO historical_data;  -- atomically swap
then...