This should come naturally playing through the career. There a few ways to build up single insults for 30 points.
The first is exploiting weaknesses. Everyone in the game has one, whether it be their age/beauty, masculinity, money, etc. Using these weaknesses adds 1.5x your insult meter.
The second is "doubling down". This is when you mention the same person/thing twice in succession. If you insult their mother in one round and see it pop up in the next try to grab it. This gives you 2x for your insult. Getting these is a bit random, especially as insults take turns and the CPU/your opponent will often take them. If you're lucky, they'll slip you one in your LB/RB options.
Next are ands and buts. I recommend using and after your first noun, unless you're doubling down. This gives you two insults for the price of one. However, if doubling down it won't count the second one for 2x. You can also use and or but to continue a longer insult.
After that there are comebacks and exclamations. Exclamations are found in the LB/RB options and end insult and are worth a bonus 3 points, unless they exploit a weakness. Comebacks end as well and are built up by levels. Level 1 seems to be worth 4 points, Level 2 around 10 and level 3 around 18. If you're really struggling, you can toss them short and weak insults and let them hit you until you reach level 3 and then unleash an epic one.
Finally there is the "..." option which continues an insult. These are risky as if your opponent insults you over 16 points, you'll get flustered and lose your partial sentence. However, a successful one can let you get 3 or 4 insults in one go, using "and" and "but"s repeatedly.
Using a few of these means to chain together points should net you big insults, which you'll also need for trophies. Standard insults seem to range from 1 for incredibly weak then 3, 5 and 9 and finally 12 for the strongest. Using multiple ways from above can result in up to 60 points for one insult.