You will need a shield that is better than the Earths atmosphere. maybe if you had a ship the had a atmosphere big enough to break up ice and asteroids that are impossible to dodge ..than yes you could reach a very fast speed I would say you could travel at 30% the speed of light and still survive in the ship, this would give you a time dilation.
When you start to travel any faster your starting to cause atoms to move through you faster causing cancer, The cosmos has fast moving particles from black holes all over.