I distinctly remember that in my early gaming days Tomb Raider had a serious competitor. I remember playing the demo of it.

Like in Tomb Raider, you were an attractive woman. She was dressed in blue and black. I think her name was Julia but I may be wrong. Her primary weapon was a slingshot, but not a regular one kids usually play with but one with which you had to swing in a circular motion in the air and then release. It looked something like this:

The point of the game was to solve puzzles, fight off enemies and jump on and off stuff, just like in Tomb Raider. The setting was quite futuristic although I think I remember some ancient world influences. The game must have been released either in late 90s or very early 2000s.

Ring any bells?