The phrase "shoot up" is often used to describe an increase in something, but there are many other synonyms that you can use instead. These include surge, skyrocket, spike, climb, soar, and escalate. If you want to convey a more aggressive tone, you can use words like blitz, assault, attack, or bombard. Alternately, for a more informal feel, you might opt for terms like amp up or crank up. Regardless of the synonym you choose, be sure to consider the context in which you're using it to ensure that it accurately reflects the situation or emotion you're trying to convey.