I have a 2003 Nissan Maxima SE and I've noticed that when I hit a sharp bump (like a shallow pothole) that the car seems to shudder or vibrate for a second. The car just hit 100k miles on the odometer about a week ago. The feeling reminds me of hitting a brick wall with a baseball bat... I suspect I might need to replace the shocks, but I'm not sure. I also am wondering if I need new shocks if I should replace all 4, or just the front, and if this is a task a shade tree mechanic could do without killing himself...
I'm going to assume that you mean hitting a bump at speed (rather than inching over it).
This sounds like a strut that's worn enough that you're pushing the strut right up against the bump stop, transferring all that energy directly into the vehicle rather than damping it on the way up.
If these struts are original and have 100K miles on them, it's pretty safe to assume that they're all done and you should replace all four.
A super quick scan of indicates that parts will cost you on the order of $100 per corner for the struts. You'll likely want to replace the strut tops and possibly the bump stops as well, possibly adding $50-ish per corner for the additional parts.
With respect to whether you could do this work yourself, it's possible but I would not recommend it for the first timer. Nothing about the labor is brain surgery but it is much harder to do without the right tools. If you don't already do this sort of thing for fun, it's worth paying to have the struts installed properly.
When I was replacing the struts on the cars at home, I needed a jack, jack stands, a good socket set, a breaker bar, a spring compressor, a set of allen wrenches, vice grips, a lot of nitrile gloves, band aids, an entire day for each car and several post-installation therapy beers.