It does have to be full odds hunt. It’s definitely possible though. My best advice is to pick a legendary beast of your choice, find a wild area where the nature you want on them goes well with the other pokemon in the area (in case one is shiny, which is more than likely to say the least), then hunt with pokemon of certain abilities in your party. If you didn’t know, legendary beasts have a base interaction rate of 1/60 in the wild, but with pokemon of certain abilities in your party you can boost the odds of encountering them up to 1/10. For suicune, water absorb and storm drain. For raikou, volt absorb and lightning rod. For entei, flash fire and blaze boost. Blaze Boost is Delta Emolga’s hidden ability for reference. The rest are easy enough to find. You should only try to hunt one beast at a time just due to the restrictions that those abilites would put on your party space, especially considering that you want to lead your party with at least one synchronize pokemon, maybe two to be safe, and then have something to false swipe and/or sleep the beasts if you’re not gonna just throw a shiny ball at them. My recommendations for areas to hunt are route 14 for suicune and raikou for timid hunts and route 17 for entei for an adamant/jolly hunt. Good luck.