KOCH ENTERS BID FOR RE-ELECTION AS 2-PARTY MAN
Mayor Koch pledged yesterday to improve city services ''vastly'' as he formally announced his candidacy for the Democratic and Republican nominations for a second term. ''Today the delivery of services moves into first place,'' the Mayor told a crowded news conference at the New York Hilton Hotel. ''I say today that we must work in the next four years to improve the quality of life in this city, and we'll do it.'' The Mayor devoted most of his statement to pointing with pride at his record, notably ''the restoration of responsible fiscal management.'' But he also interjected often the element of running against his record on city services. He tried here to head off the opposition by promising even better times ahead.