What makes this tricky is that swatting and grabbing share the same button (
). Before using your lasso, look for a white light on the grapple point. This signals that you will use your lasso instead of swatting.
If the mosquitoes swarm you, jump around to clear them for a few seconds.
Once you're past all of the mosquitoes, just finish the level, and the achievement will pop.
Please, let me know if you have any questions!