It is a humbling and overwhelming experience to box again an aggressive opponent who just keeps coming. There are ways to deal with such a situation and you can practice this in your training.
1. Keep your hands up at all times. This is pretty obvious but you should keep your "shield" up as you engage. You want to make your self an invulnerable target and the windows to strike you should be small and hard to find. You will have to fight back, and you will want to always put your hands back to protect yourself and keep your defense tight so you can be relaxed as you deal with the pressure.
2. Use footwork when needed. You will need to move, but you don't want to "run" away from the pressure because you will eventually tire and a forward-moving fighter likes chasing you down. Learn how to be right outside of your opponent's range and when you need to you can shuffle or backpedal to get space. You do not want to get caught on the ropes at all, so if you are pushed back you want to find any opportunity to side step away from the pressure to set up angles to counter and change the momentum. Be light on your feet to make them have to work hard to set up their punches.
3. Stay relaxed and make them chase you to where they can be countered. They say pressure burst pipes so you don't want to become overwhelmed by the constant attack. Move efficiently with balance so you can put them in positions where you can strike. A forward-moving fighter will collide with your punches, increasing the power of your punches. Set them up to run into your punches and utilize good timing to make them pay for being aggresive. Be slick and in control.
4. Be first and punish when they step in. Be a step ahead of their movement keep the jab present. Many aggresive fighter will load their shots heavy so strike as they set it up so they are not allowed to fully impose their offense. Don't be the "prey" and let them know you have just as much fight as them. When they step in let them know there is a price to be paid. Don't allow them to freely walk into your space without consequences. Be defensively aggresive.
5. Use feints and jabs outside of their distance and counter the advances. Keep them thinking and second-guessing their advance by keeping a jab in their face. Stay right outside of their distance and don't stand right in from of them so they can set their feet and deliver a barrage of punches. Proper feints will cause them to react either offensively or defensively where you can counter with power punches. "Poke the bear" and punish them every time they "swipe" at you. Keep your hands loose and swift and keep the defense tight and feet moving.
6. Keep them turning and pull them into your punches. You don't want to move in straight lines, especially backwards where they can build momentum to overpower you. One general rule is don't step backward more then once. Use sidesteps and shuffling to force them to turn. A turning opponent will have to work harder to set their feet to throw punches. As you turn them, use their chasing momentum to pull them into your punches. Flank them and don't stay right in front of them or they will eventually jump on top of you and smother. Shift your weight smoothly and rhythmically side to side so they cannot line their punches up. If you know how to switch stances, utilize it to create space for shots and different looks that they will have to deal with.
7. Catch and counter hard. You won't evade everything they come with so you want to catch their shots with a strong base and withstand what they bring with a tight guard. You need to answer their punches with your own and they should be hard and accurate so you get their respect. In dealing with a "bully" you will eventually need to stand your ground and strike back. Show them you mean business and keep you chin down, elbows in, and make your hands "heavy".
8. Be willing to fight inside and smother and tie them up when you need to. Sometimes the safest place in a tornado is in the eye of the storm. You want them also to feel your presence and you won't be able to keep a pressure fighter off you for the whole time. They are most powerful at the end of their punches where they can step into them. Smother them so they will be forces to try to create space, halting their forward momentum. Smother them so they arms are pinned and locked up and use your weight on areas like the shoulders that manipulate their balance. Tie them up and be active in the clinch, breaking up their forward rhythm. Don't be rigid on the inside. Like Bruce Lee said, "Be like water" and flow with their movements and crash back with short stabs to the body.
9. Back them up to keep them on their back foot. Eventually you got to stand up to a bully. They apply that pressure because many times they don't like that pressure themselves. If your jab, movement and angles aren't working you may just want to take it to them and defensively apply your own pressure. Put them on their back foot where they may not be comfortable. A good example is where Canelo walked down GGG in their second match. GGG didn't have as many answers because he was used to being a forward momentum fighter. Walk them down with combinations and smother and tie them up to prevent them from countering. Do not step back away from them, but escape of the side if you want to re-establish your range.
Here is a masterful fight by Floyd Mayweather against Diego Corrales where he used his jab to keep him off and taking it him with combinations and moving effectively.