In the beginning of a research program students (like me) may be lazy or find things hard and do things that make their supervisors get angry such as not completing specific job in the right time. They may be strongly criticized by their supervisors and their supervisors may get an idea that these students are not good enough. How can students change this idea that is in the head of their supervisors? What should they do?
The same way you would change anyone's perception of you for any other reason: Prove them wrong.
If you started out lazy, then kick yourself into high gear: Get tasks done ahead of time; predict future work, and get it done before it's asked for. Turn out quality work at a high pace. This sounds hard because it is. Unfortunately, you may have burned good-will at this point, and you need to rebuild it.
If you found things hard, or found that the supervisors expectations of velocity were unreasonable, discuss it with your supervisor. Discuss what background she may not know you have missed, discuss how you spent your time, and why things didn't get done fast enough.
Key here is the relationship. Your relationship sounds like it's on rocky ground, and if you're in it for another 3-5 years, then don't underestimate how much effort you're going to need to making sure that relationship doesn't break down.
... and, if your supervisor is an experienced, mature person, while they may have been irritated by sub-par "performance", such things should not completely surprise them. People in grad school are in a transition time in life, not only regarding the stresses of grad school, etc., and have not yet "arrived" themselves at the mature professional state they will (hopefully) reach. In particular, helping people get to that state is part of a supervisor's job with grad students (and probably any senior person in any professional situation).
So, while it's not good to have under-performed to the extent of setting-off your supervisor, and not a "good start", there should be much room for "forgiveness", if you can take a lesson from such a scenario, etc.