I didn’t realize when I chose it—to be honest, if I don’t have a theme I’m following or a request to fulfill, I choose these monsters more or less at random, although I tend to favor the old-school ones—but the manticore is the first creature I’ve encountered whose tactics are already laid out in the Monster Manual flavor text:
A manticore begins its attack with a volley of tail spikes, then lands and uses its claws and bite. When outdoors and outnumbered, it uses its wings to stay aloft, attacking from a distance until its spikes are depleted.
Given the manticore’s stat and feature profile, these tactics make sense. The Tail Spike is a strong attack with good damage and a generous range, and the manticore can hurl three in a single Multiattack action. Its Strength, Dexterity and Constitution are all very high, suiting it equally for ranged and close-in combat. It stands to reason that it would use its strongest, safest attack first, then close in to finish off injured enemies.
This part makes a little less sense, though this is a monstrosity we’re talking about, after all, so some of its behaviors are going to be weird:
A manticore isn’t particularly bright, but it possesses a malevolent nature and the ability to converse. In the course of attacking, it denigrates its foes and offers to kill them swiftly if they beg for their lives. If a manticore sees an advantage to be gained by sparing a creature’s life, it does so, asking for a tribute or sacrifice equal to its loss of food.
The manticore’s Intelligence is 7; its Wisdom, however, is 12. I don’t think it would be possible to trick a manticore into accepting a bad deal. In fact, I think it would have very little imagination with respect to what might constitute a good deal. The only thing that would be more appealing to a creature like this than food would be more food, perhaps a steady and easily obtained supply of it. A greater challenge, though still possible, would be offering to eliminate a known territorial rival (the MM lists chimeras, griffons, perytons and wyverns as being among these). I think a manticore is simply too dumb to recognize the value of anything beyond food and territory.
As for target selection, a manticore will be indiscriminate. As a Large creature with formidable physical ability scores and low Intelligence, it sees all player characters as equally weak and doesn’t distinguish between ranged fighters and melee fighters or spellcasters and non-spellcasters. A PC who can deal it 20 hp or more of damage in a single turn will certainly get its attention, but that’s as likely to enrage it as it is to make it hesitate.
A few final notes: The manticore has darkvision, so it will have an advantage over many PCs when attacking at night or twilight. It has a land speed of 30 feet but a flying speed of 50 feet, so it will move by leaping and won’t be hindered by difficult terrain; furthermore, it will probably live and hunt in difficult terrain, where its prey will be slowed. It will flee when seriously injured (reduced to 27 or fewer hp) by Dashing away through the air—it’s not smart enough to Disengage, and it’s tough enough that it normally wouldn’t have to, anyway. And finally, the MM flavor text notes that manticores often hunt in packs, so despite having a challenge rating of only 3, they may still make good opponents for intermediate-level PCs . . . although it doesn’t seem likely to me that a manticore encounter would include more than four or five of them.