I've been given this same feedback before! I think analytical is a hard word to understand (or at least it was for me!) because it doesn't actually tell you about the substance the firm is looking for and so really doesn't give you much to go off of.
What I've taken it to mean since that initial feedback is: you can pick out the main issues, you can think about the effects these issues will have on the client, and most importantly you can offer solutions or come to a decision on the client's behalf. Don't just offer the advantages/disadvantages of the outcome, but balance both and provide an answer (because that's what clients come to lawyers for)
The way you present your answer is also important. The most important issues should come first and ideally you're grouping issues that are interrelated together. This again involves that "analysis" element because you have to think about how sometimes very separate issues are related and why they should be addressed together.
Something I always recommend to people struggling with analysis specifically is to try out some consulting case studies (loads of free ones online!). The scenarios are incredibly sparse (and imo slightly less straightforward than law firm case studies) which forces you to analyse the information given from different angles a lot more. It also prepares you really well for the law firms that don't use strictly legal case studies.
Jacob's article has much more detailed advice and examples, but I hope this helps anyway!