To attempt something is, at root, to test it. The word descends from Latin attemptāre, composed of ad- ('towards') and temptāre ('to feel, to test, to try'). The original meaning was closer to probing than striving — you attempted a task the way you might test a bridge before crossing it.
Latin temptāre is the ancestor of both attempt and tempt. The connection is clearer than it first appears: every temptation is a test. In biblical Latin, the devil does not lure — he tests. The temptation of Christ in the wilderness was a trial of resolve, and the Latin Vulgate uses temptāre for exactly this scene.
The same root produced tentative — still in the testing phase, not yet committed to action. And contempt comes from contemnere, a related form meaning 'to scorn' — originally, to examine something thoroughly and find it worthless.
Old French softened attemptāre into atempter, and Middle English adopted it in the 14th century. The legal sense developed early: an attempt at murder was a test of intent that fell short of completion. This legal distinction — between attempting a crime and committing one — preserves the original Latin sense of testing without finishing.
The word retains a humility that 'try' lacks. To attempt acknowledges uncertainty. You attempt the difficult, the doubtful, the untested.