There are total 24 different modes in Chester's Choice. And just to be safe, be sure you have cleared all other feats that unlocks pallettes so Chester has more modes to keep randomly cycle. So, to begin with, in the option mode, you must select Chester's Choice (the one you can select Showdown, Treasure Clash or Chester's Choice). Whenever you start a match, you'll be given 4 different random modes. Here's how it works to get the achievement.

Each time Chester give you a random mode, you must WIN the match. Say, for example, you randomly got Covert Combat mode. Win the match and that counted as one seen view! And it would be best to write down which mode you have won, so you can keep track and restart another match to get the mode you haven't won yet. For that, you have to play 20 different modes matches. To make it easy and fast, set the AI to 1, so it's an easy win for each match. That's how I got it. So I hope this help you too!

24 Different Modes

01 - Fight of Fate
02 - One Hit KO
03 - Field of Honor
04 - Showdown
05 - Timeless Battle
06 - Fairy Frenzy
07 - Treasure Clash
08 - Birder Paradise
09 - Beeto Breach
10 - Repeller Rally

11 - Just Gems
12 - Giants
13 - Big Hits
14 - Covert Combat
15 - Sudden Death
16 - Hyper Brawl
17 - Eggstravaganza
18 - Duel of Zorix
19 - Duel of Bombs
20 - Bombs Away

21 - Single Stock
22 - Bubble Bonanza
23 - Hurricane
24 - Winner Takes All