first, key, main, major, primary, prime, principal
second, secondary
broad, overall, overriding, ultimate
limited, narrow
long-term, short-term
clear, specific
important
stated
The legislation has failed to achieve its stated objectives.

desired
common
The two groups are pursuing a common objective.

economic, educational, environmental, military, political, strategic
business, course, learning, mission, policy, research

have
accomplish, achieve, attain, complete, fulfil/fulfill, meet, reach, succeed in
The department needs more money to achieve its objectives.

fail in
agree, define, establish, formulate, identify, set, specify
a set of agreed objectives
We need to establish a clear objective.

declare, state
promote, pursue, support

in an/the objective
The party is radical in its objectives.

objective of
We succeeded in our prime objective of cutting costs.

be, seem
remain

truly, very
completely, entirely, purely, totally, wholly
It is impossible to be completely objective.

fairly, reasonably
apparently (esp. BrE), seemingly (esp. AmE)
supposedly

Objective is used with these nouns:
analysis, assessment, criterion, description, evaluation, evidence, judgement, manner, measure, measurement, observer, opinion, perspective, point of view, reality, standard, standpoint, test, truth, viewpoint